This view is referred to as the "quasi-incarnation of the Spirit."
Apparently, Maximilian Kolbe (a Roman Catholic "saint" from the 20th century) is the person most closely associated with this view. Dwight Campbell explains:
In other writings the Polish friar attempts to describe Mary's deep, intimate union with the Third Person of the Trinity from her conception, by calling Mary the "quasi-incarnation" of the Holy Spirit. He is careful to stress that this union "is not of the same order as the hypostatic union linking the human and divine natures in Christ"; for he repeated often that the Holy Spirit does not dwell in Mary in the same way in which the Eternal Word is present in the sacred humanity of Jesus.The need for these caveats up front hints at what is coming. Campbell further explains:
With the term "quasi-incarnation" Kolbe means that Mary is so much like (quasi) the Holy Spirit, in that she reflects the Third Person of the Trinity especially in two qualities or attributes: receptivity and fruitfulness. The Holy Spirit is the Fruit of the Father and the Son. He was "eternally conceived," if you will, as the Fruit of the all-pure love which has forever flowed between the Father and the Son. He receives the mutual love of the Father and the Son and eternally fructifies it within the inner life of the Trinity. Mary's sinlessness from conception is the fruit of God's love. At Mary's conception the Holy Spirit conformed her to himself. The Blessed Virgin, by reason of the singular grace of her Immaculate Conception, is totally receptive to the love of God. At the Annunciation she receives God's love and in cooperation with the Holy Spirit makes that love fruitful — infinitely so — in conceiving the Incarnate Word.I'm sure my Orthodox friends will be quick to notice that Kolbe's view springs out of his double-procession view of the Holy Spirit, something traditionally rejected in Eastern Orthodoxy. Moreover, it is odd to make the Holy Spirit the "fruit," regardless. Wouldn't the the Son be a better example of uncreated fruit?
Campbell quotes Kolbe as saying:
[T]he Holy Spirit manifests his share in the word of Redemption through the Immaculate Virgin who, although she is a person entirely distinct from him, is so intimately associated with him that our minds cannot understand it. So, while their union is not of the same order as the hypostatic union linking the human and divine natures in Christ, it remains true to say that Mary's action is the very action of the Holy Spirit.Notice this claim - Mary's action is the action of the Holy Spirit. How much closer to making Mary a fourth person of the Trinity could one get?
When we reflect on these two truths: that all graces come from the Father by the Son and the Holy Spirit; and that our Holy Mother Mary is, so to speak, one with the Holy Spirit, we are driven to the conclusion that this Most Holy Mother is indeed the intermediary by whom all graces come to us.Notice how in this picture, Jesus is no longer the mediator of all graces, Mary is. This exaltation of Mary comes not only at the expense of the Spirit, but of the Son as well.
Dr. Mark Miravalle (a professor of theology and mariology) video in which he tries to explain Kolbe's "unique contribution" to mariology. A big chunk of the video explanation is actually a rant against contraception, but that is what it is. The remainder confirms much of what we read above.
He points out that Kolbe calls the Holy Spirit the "uncreated Immaculate Conception." Why wouldn't that be Jesus? Miravalle does not tell us. According to Miravalle, Kolbe argues that the Holy Spirit and Mary are spouses (!). Moreover, the allegation is that Mary and the Holy Spirit work together to "bring forth the graces leading the redemption and the fruit of the redemption." Kolbe actually says that calling their relationship spousal is "too weak" to describe their relationship.
In a follow-up section, Miravalle explains that the better analogy is the hypostatic union. Kolbe claims that, as we saw above, the Holy Spirit "in a certain sense was incarnate in Mary." The distinctions he makes is that the Holy Spirit is not actually incarnate, and that the Holy Spirit is a different person from Mary. However, according to Miravalle, Kolbe takes the position that "if the Holy Spirit were to become incarnate, he would be Mary."
But it goes farther than that. Miravalle attributes to Kolbe the idea that "the Holy Spirit acts only through Mary his spouse." That, of course, leads to the idea that Mary is the "mediatrix of all graces." But notice that Miravalle's way of expressing Kolbe provides the flip-side to the coin we saw above. Above, all of Mary's acts are the Holy Spirit's acts, but now all of the Holy Spirit's acts are Mary's acts. The two become functionally indistinguishable, and again Jesus as mediator is pushed out of the picture.
It should not be surprising that Kolbe's devotional life expressed Mariolatry. For example, he apparently composed the Immaculata prayer, which states:
O Immaculata, Queen of Heaven and earth, refuge of sinners and our most loving Mother, God has willed to entrust the entire order of mercy to you. I, (name), a repentant sinner, cast myself at your feet, humbly imploring you to take me with all that I am and have, wholly to yourself as your possession and property. Please make of me, of all my powers of soul and body, of my whole life, death and eternity, whatever most pleases you.(source)
If it pleases you, use all that I am and have without reserve, wholly to accomplish what was said of you: "She will crush your head," and "You alone have destroyed all heresies in the whole world." Let me be a fit instrument in your immaculate and merciful hands for introducing and increasing your glory to the maximum in all the many strayed and indifferent souls, and thus help extend as far as possible the blessed kingdom of the most Sacred Heart of Jesus. For wherever you enter you obtain the grace of conversion and growth in holiness, since it is through your hands that all graces come to us from the most Sacred Heart of Jesus.
V. Allow me to praise you, O Sacred Virgin
R. Give me strength against your enemies
Notice that he says that the "entire order of mercy" is entrusted to Mary and that "all graces come to us" through Mary's hands. At least Jesus is mentioned, but he is mentioned on the other side of the transaction - not as a mediator, but as the one needing Mary's mediation with mankind.
Notice that he casts himself at Mary's feet and gives himself to her. Notice that he relies on an interpretation/mistranslation of Genesis 3:15 that substitutes Mary for Jesus as the one who crushes the serpent's head. Notice that he attributes to Mary the destruction of "all heresies."
The "daily renewal" prayer for the same adds to the errors:
Immaculata, Queen and Mother of the Church,Notice that this is not just an acknowledgment of prayers to Mary, but also an offering of "all my ... sacrifices". The only way in which he does not treat Mary as divine is to explicitly say "you are divine."
I renew my consecration to you for this day and for always, so that you might use me for the coming of the Kingdom of Jesus in the whole world. To this end I offer you all my prayers, actions and sacrifices for this day.
The parallels made to the divine don't stop there. Deacon Antonio explains:
The infinite love that Jesus had for the Father made him a special image of the Father; it made him an “icon” of the Father. An icon is not simply an image; it is a window into a spiritual reality. Jesus essentially told Philip, “If you know me, you know the spiritual reality of who the Father is”.Notice the comparison - like Jesus is the Icon the Father, Mary is the Icon of the Holy Spirit. But the fact that Jesus is the Icon of the Father proves that Jesus is divine. So, what should we gather from Mary's Icon-status? Well, clearly she is being treated in nearly every way as if she were a fourth person of the Trinity, except to actually say that she is a fourth person of the Trinity.
Mary has been called the Icon of the Holy Spirit, no doubt, because of the profound love that united her to the Holy Spirit throughout her life. As an icon of the Holy Spirit, Mary reveals the Holy Spirit to us. And we should also see Mary in the Holy Spirit. Saint Maximilian Kolbe believed this, because he called the Holy Spirit the “Uncreated Immaculate Conception” and he called Mary the “created Immaculate Conception”.
My friend David King provided an interesting patristic response to the idea that Spirit becoming incarnate:
Gregory of Nyssa (c. 335-95): [Apollinarius] claims that this man is from heaven because the heavenly spirit took on flesh. Where does scripture speak of such a thing? Which author of the sacred text says that spirit became incarnate? Neither the Gospel nor the great Apostle [Paul] has taught us such a thing. Instead, the Gospel proclaims "the Word became flesh" [Jn 1.14] and the Spirit descended in the form of a dove [Mt 3.16]. Nothing is said here of the Spirit becoming incarnate with regard to the mystery of our faith. "His glory has dwelt in our land" [Ps 84.10]. "Truth has sprung from the earth" [Ps 84.12]. "God has manifested himself in flesh" [1Tm 3.126]. "Righteousness has looked down from heaven" [Ps 84.12]. These and other examples show that the divinely inspired scripture does not mention the Spirit's incarnation. (Translation via here)
Greek text: Τοῦτον δέ φησιν ἐξ οὐρανοῦ διὰ τοῦτο καλεῖσθαι, διότι τὸ πνεῦμα τὸ οὐράνιον ἐσαρκώθη. Τίς Γραφὴ ταῦτα λέγει; εἰς τίνα τῶν ἁγίων ἀναφέρει τὸν λόγον, ὅτι πνεῦμα ἐσαρκώθη; Οὐχ οὕτως παρὰ τῶν Εὐαγγελίων ἠκούσαμεν, οὐχ οὕτως παρὰ τῆς μεγάλης τοῦ Ἀποστόλου φωνῆς ἐδι δάχθημεν, ἀλλʼ ὅτι μὲν ὁ Λόγος σὰρξ ἐγένετο, λέγει τὸ κήρυγμα καὶ ἐν εἴδει περιστερᾶς τὸ Πνεῦμα καταβῆναί φησιν ἡ εὐαγγελικὴ ἱστορία· σάρκωσιν δὲ πνεύματος οὐδεὶς εἶπε τῶν τῷ πνεύματι λαλούντων μυστήρια. Ἡ δόξα κατεσκήνωσεν ἐν τῇ γῇ ἡμῶν· καὶ Ἡ ἀλήθεια ἐκ τῆς γῆς ἀνέτειλε· καὶ Θεὸς ἐφανερώθη ἐν σαρκί· καὶ Δικαιοσύνη ἐκ τοῦ οὐρανοῦ διέκυψε· καὶ ἄλλα τοιαῦτα πολλά. Πνεῦμα δὲ σαρκούμενον ἡ θεόπνευστος οὐκ οἶδε γραφή. Adversus Apollinarem, §12, PG 45:1145.
Of course, Kolbe doesn't say the Holy Spirit was incarnate, only "quasi-incarnate." This claim, like the higher claim, fails the test of Scripture. Scripture does not teach that Mary was the spouse of the Holy Spirit (she was the spouse of Joseph) or that Mary is quasi-incarnate. It was not the Holy Spirit who forgot Jesus in Jerusalem. It was not the Holy Spirit whose request to see Jesus was met with him stretching forth his hands to his disciples and saying, "Behold my mother and my brethren!"
Kolbe's views aren't just wrong, they're blasphemous. By associating Mary with the Holy Spirit in this way, Kolbe's views unduly exalt a mere creature and unduly diminish the work of Jesus and the Holy Spirit.