No it doesn't.  Trent teaches that one cannot be justified without the Sacrament or the desire for it.  That last part is unclear and can be interpreted either way.  I'm torn about which way it goes, but lean toward the reading that both are required for justification.

As for Baptism being OPTIONAL, that's blatantly untrue that "no one [of BODers] believes Baptism is optional".  Vast majority of BoDers do hold that it's optional, a nice to have, but not necessary by necessity of means for salvation.  Majority of BoDers are Pelagian heretics.

That's already been addressed above.  Apart from the fact that your'e conflating BoB ad BoD, as most BoDers do, there's no evidence that St. Emerentiana was not baptized.  During times of persecution, the Church generally commanded that catechumens be baptized, even though they continued to be considered catechumens, continued in their instruction, and were not allowed to receive the Sacraments until they completed the instruction.

No, I say neither are infallible, what gave you the idea that I considered my references to be infallible?

But, yes, let's jump to Trent.  I'll come back and deal with Innocent II and Innocent III later in more detail.  Trent did not teach that souls could ultimately be saved via justification by desire, and the language makes it unclear whether it was an either ... or proposition, or a both were required proposition.  I think it was more likely the latter, for reasons I can illustrate later.

1) Nowhere does it say that she was not baptized.  It just says she was a catechumen and that she was baptized by her blood.  Elswhere it is said that a priest, St. Lucian, was also baptized by his blood.  He was obviously baptized also.

2) Roman Martyrology is not infallible.  There's a Pope on record saying one had to be careful about it lest some of the stories be found spurious and bring the Church into ill repute.

So the case of St. Emerentiana is inconclusive.

That last sentence was unclear to me in your original because of your placement of the comma in front of ", as St. Alphonsus teaches it".

Yes, it's a double negative in Trent.

We cannot have a wedding without a bride or a groom.  [Both are required.  If either is missing, it's a no-go.]
I cannot write a letter without a pen or a pencil. [Either one suffices.]

Latin has the same ambiguity, as this a logical, not a grammatical problem.

But as a proof text for this, immediately after this phrase, Trent cites Our Lord that "unless one be born again of water AND the Holy Spirit".  Water hearkens to the "laver" and the "Holy Spirit" to the votum ... as Trent just explained how the Holy Spirit inspired the dispositions necessary for Baptism ... which is how Catholic Encyclopedia defines votum (and not just as simple "desire").  So this would be like saying, "No one can be justified without water or else the Holy Spirit, because Our Lord taught that one cannot enter the Kingom without water AND the Holy Spirit."  That would make it nonsensical.

Where Trent does clearly state that perfection contrition + the votum suffices for restoration to justification (in a baptized individual), Trent makes it very clear, using the disjunctive "vel ... vel" (a non-exclusive "either ... or" ... or both) and in another place "saltem in voto" (at least in desire).  And Trent could easily have used the same expression here, but didn't, just using a simple "aut" ("or").

Other problems with "aut" (an exclusive disjunctive, tending to mean either ... or, but NOT both) is that it would imply that one could be justified by EITHER the Sacrament OR the votum, meaning that one could be justified by just the Sacrament without also having the "intention", but that's actually anathematized by Trent, which teaches that the Sacrament does not justify without the intention to receive it (recall that this section is speaking exclusively about adults, not infants).

Another issue is that if Trent teaches that there can be no justification without the Sacrament or the desire, that effectively rules out Baptism of Blood as being something separate from Baptism of Desire and that does not reduce ot it.  So St. Alphonsus, by holding to a Baptism of Blood that works "quasi ex opere operato" would be contradicting this teaching of Trent.  So the so-called "Three Baptisms" must now be considered "Two Baptisms."

Ah, but you might say, this just means that even someone with BoB has to have the votum for it, i.e. must ALSO have the votum for it.  That completely undermines the interpretation of "aut ejusdem voto" being an exclusive or ... and REINFORCES the interpretation that this means (whether you receive the Sacrament ... or martyrdom ... you must ALSO have the desire for it).

Finally, Trent made clear what the Council intended to define ... by putting the rejection of certain propositions in the anathemas section (the Canons).  BoD nowhere appears in the Canons.  Nowhere does Trent teach, "If anyone sayeth that a man cannot be justified without the votum alone, without having actually received the Sacrament, let him be anathema."  Just reading that sentence makes it sound aburd.  Church would never defined such a thing.  She has tolerated BoD speculation, but there's no evidence that BoD was revealed, and would never issue this type of absurd anathema.  One reading, agreed to by a BoDer here, just sees this as saying, "if you say that the Sacraments are not required ... at least by way of desire ... for salvation, you're a heretic".  In other words, it's saying that we must HOLD that at the very least there must be the votum for the Sacrament, but falling short of saying that we must hold that it CAN justify by itself.  If read this way, it would confirm that the Dimonds are wrong for considering BoD to be heresy.

So ... there are just too many problems with claiming that Trent positively defines that it is possible to be justified (much less saved) without actual reception of the Sacrament.  It's clear that Trent does not condemn the notion (I know that Stubborn disagrees, but that's his opinion), but neither does it positively define it.  Trent did fall short of teaching that the ACTUAL reception of the Sacrament is required for justification, but it also did not positively teach that the VOTUM along could certainly suffice.

As I mentioned, it was actually a pro-BoDer who cited some post-Tridentine theologians who made the justification vs. salvation distinction, holding for instance that infidels could be justified but not saved.  This harkens back to St. Ambrose who taught that it might be hoped that someone cold be "washed, even if not crowned" (that would be akin to justification but not salvation), being in Limbo (as Dante thought of Saladin) but not enjoying the Beatific Vision.

Also, for something that's de fide, I've never seen so much disagreement about the details.  You have a different understanding of BoD for almost everyone who holds it.  To whom can it apply, under what conditions, etc.?  Some apply it only to catechumens, others to infidels, others to heretics (even the baptized ones, strangely enough).  Some say that explicit faith in the Holy Trinity and incarnation are required, others that it suffices for someone to believe in a Rewarder God.  Unfortunately, the greatest common denominator among all these flavors is that "the Sacrament of Baptism is not necessary for salvation" ... which is of course heretical.  We do not give the assent of faith to a "phrase" or a "word".  We assent to propositions.  I do not believe in "BoD", but I believe some proposition ... which is entirely unclear.  Which other dogma can we say this about, that we have no idea WHAT it is we have to believe about it.  Surely Trent would have clearly defined the propositions that must be believed, and would have condemned the contrary propositions with anathemas.

So I personally do believe in a BoD, in the sense of a justification by "vow / intention / will" (as "desire" is too weak), but I do not believe that this state of justification can suffice for entry into the Beatific Vision (the "crowning", the "glory", the "seal").

I hold that it is the Sacramental Character that impresses upon the soul the likeness of Our Lord, and causes God to recognize us as His (adopted) sons and adopted members of the Holy Trinity.  Also, the beatific vision is something beyond the capacity of our nature, so this character also endows the soul with the supernatural faculty to be able to see God as He is (a faculty we lack by nature).  So it is much more than some non-repeatability marker that some in Heaven have and others do not.  I hold it to be essential for the Beatific Vision.[/i]

Finally, another issue I have with extending BoD beyond a catechumen is that it leads directly to the Vatican II ecclesiology.  Without this extended BoD, you could never have had Vatican II.

MAJOR:  There's no salvation outside the Church.
MINOR:  Protestants, Jєωs, Muslims, and infidels can be saved.
CONCLUSION:  Protestants, Jєωs, Muslims, and infidels can be inside the Church.

So now we have the Vatican II franken-church here, which consists not only of Catholics but also of Prots, Jєωs, Muslims, infidels,  Nor can one say that they suddenly become "within the Church" at their death, since one of the EENS definitions clearly teaches they must be joined to the Church BEFORE their deaths.