In the session on Justification, Trent writes:
CANON IV.-If any one saith, that man's free will moved and excited by God, by assenting to God exciting and calling, nowise co-operates towards disposing and preparing itself for obtaining the grace of Justification; that it cannot refuse its consent, if it would, but that, as something inanimate, it does nothing whatever and is merely passive; let him be anathema.
Notice the key word there "co-operates." That means man acting with God. It is a denial of monergism and a denial of sola gratia.
And we are not stuck alone with Trent's fourth canon, for the same thought is expressed:
CHAPTER V. On the necessity, in adults, of preparation for Justification, and whence it proceeds. The Synod furthermore declares, that in adults, the beginning of the said Justification is to be derived from the prevenient grace of God, through Jesus Christ, that is to say, from His vocation, whereby, without any merits existing on their parts, they are called; that so they, who by sins were alienated from God, may be disposed through His quickening and assisting grace, to convert themselves to their own justification, by freely assenting to and co-operating with that said grace: in such sort that, while God touches the heart of man by the illumination of the Holy Ghost, neither is man himself utterly without doing anything while he receives that inspiration, forasmuch as he is also able to reject it; yet is he not able, by his own free will, without the grace of God, to move himself unto justice in His sight. Whence, when it is said in the sacred writings: Turn ye to me, and I will turn to you, we are admonished of our liberty; and when we answer; Convert us, O Lord, to thee, and we shall be converted, we confess that we are prevented by the grace of God.
Notice the key words (for our consideration): "they ... may be disposed through ... grace, to convert themselves to their own justification, by freely assenting to and co-operating with that said grace...."
This is a rather clear denial of salvation by grace alone. Thus, the answer to the title question is a resounding NO!
Trent is not, however, advocating Pelagianism. Trent is not making an assertion that grace is unnecessary. The paragraph insists on the essential presence of grace. That is very good. It is laudable that Trent did not teach Pelagianism.
Nevertheless, Trent does not teach salvation by grace alone. If one recognizes that Scripture teaches salvation by grace alone, one needs to make a decision:
1. Either believe Scripture's testimony, or
2. Believe Trent's testimony.
The former way is the way of the Reformers, and the latter way must be the way of any consistent Catholic. Now, note: I have not, in this post, shown that Scripture teaches that salvation is by grace alone. If I were debating the matter of what Scripture teaches, I would want to address that issue.
Instead, I am simply addressing in this post what Rome teaches. Why would I do that? I would do that because there are certain men out there in the Internet who would like people to believe that Rome teaches salvation by grace alone.
And guess what: you can find statements praising the phrase "sola gratia" from places like the Vatican's official web site. There is a modicum of veracity to such a claim. However, given what Trent dogmatically defines:
1) Either the Vatican's official web site (and the people speaking through it) mean something different by "sola gratia" than monergism (i.e. they are, in effect, equivocating); or
2) Even the pope makes mistakes, and an affirmation of sola gratia (the teaching that men are saved by grace alone, and not at all in any way by human merit) is necessarily a mistake because it conflicts with Trent's teaching on justification.
In other words, Trent as a putatively ecumenical council (though dominated by Italian and Spanish bishops, and devoid of Reformed and Orthodox bishops) has greater ecclesiastical authority than anything one can find in speeches made by modern ecumenical bishops, archbishops, cardinals, or even popes.
If this were a card game, Trent is a trump card, beating out even such "official" documents as the Catechism of the Catholic Church, and - of course - beating out the writings of Internet apologists.
Catholics: you're stuck with Trent. You cannot change it. You cannot ignore it. If you want to be Catholic, you have to agree with Trent.
I'm bound to hear the objection that I simply don't understand Trent. Why am I so sure that I'll hear that objection? Because it is the same tired objection I hear every time a Catholic person disagrees with me about Catholic doctrine, or a Mormon person disagrees with me about Mormon doctrine (though substitute "Book of Abraham" for "Trent"), or an Orthodox person disagrees with me about Orthodox doctrine (though substitute "Chrysostom" for "Trent") etc. etc. etc. ad nauseum. I've already blogged about this syndrome elsewhere (link). It's a self-defeating argument for those that deny sola scriptura on the allegation that scripture is inscrutable.
But, to be clear, let me point out that at least some Catholics agree with me that Catholic doctrine rejects the Reformed doctrine of sola gratia: Prof. Dr. Josef Seifert, Rector of the International Academy of Philosophy in Liechtenstein, internationally acclaimed philosopher, and member of the Pontifical Academy for Life. Dr. William Marshner, chairman of the Theology Department at Christendom College (pointing out that "sola gratia" can only accepted by Catholics with respect to initiation towards justification).
Why then do we also see Catholics, like Mark Brumley (link) suggesting that the Reformation was right about sola gratia? The most charitable answer is that the matter is clear from Scripture, and consequently it is hard to try to continue to deny its truth. Christians realize that Scripture is the ultimate infallible authority we have today, supreme over Trent and over anything anyone's religious leaders may say. If Scripture says it, we must believe it, and if Trent disagrees, the worse for Trent.
And, of course, to reject Trent is to cease to be Catholic.
May God give Christians wisdom to accept the truth of sola gratia,
UPDATE: Apparently at least one thing was not clear from the post above. If one defines "sola gratia" to mean something other than monergism, then of course Trent can be made to accommodate "sola gratia" under that different definition. In fact, one can assert that the RCC teaches "sola scriptura" as well, as long as one is careful to redefine sola scriptura to mean something other than what the Reformers meant by it.