This question made me think about the movie versions of the 7th book.
In Deathly Hallows Part II
Voldemort has Nagini attack Snape because Voldy thinks that Snape has the Elder Wand's allegiance. We know that Snape didn't actually have the allegiance, Draco did (and by then Harry did) and his plan had failed.
But if Voldy's plan had succeeded with Snape, would he have gotten allegiance?
Since voldemort didn't kill Snape, Nagini did...
The following is quoted in the answer to the question you linked to:
Believers in the Elder Wand, however, hold that because of the way in which it has always passed allegiance between owners – the next master overcoming the first, usually by killing him – the Elder Wand has never been destroyed or buried, but has survived to accumulate wisdom, strength and power far beyond the ordinary.
Godelot is known to have perished in his own cellar, where he was locked by his mad son, Hereward. We must assume that Hereward took his father’s wand, or the latter would have been able to escape, but what Hereward did with the wand after that we cannot be sure.
Tales of Beedle the Bard - Page 103 - Bloomsbury Edition
That implies that any "defeat" of one wizard by another (trap, spell, or other means) would transfer the allegiance of the wand. So given Nagini is effectively part of Voldemort, and definitely a minion of his, I would say that it's quite likely that it would have worked.
No, Voldemort would not have been able to master the Elder Wand under any circumstances because only those who are capable of facing death can master the Elder Wand. JKRowling.com
ETA: In addition to the above info cited from JKR's website, and the quotes I included in my comments (which I will add to this answer), I have some additional thoughts on why Voldemort is unable to face death, thus making it impossible for him to ever truly master the Elder Wand. I know you've already chosen your answer, so this is just food for thought for others who might read this in the future.
‘He was more afraid than you were that night, Harry. You had accepted, even embraced, the possibility of death, something Lord Voldemort has never been able to do.' Albus Dumbledore - Deathly Hallows - Page 569 - British Hardcover (page 711 US Hardcover)
And:
'You are the true master of death, because the true master does not seek to run away from Death. He accepts that he must die, and understands that there are far, far worse things in the living world than dying.’ Albus Dumbledore to Harry Potter - Deathly Hallows - Page 577 British Hardcover (pages 720-721 US Hardcover)
From The Elder Wand at The Pensieve:
Voldemort not only did not obtain the wand by defeating its master, but he also, as JKR has told us time and again, was incapable of facing death. He created seven Horcruxes to prevent his death. Even his dying bit of soul, glimpsed by Harry in King’s Cross, was cowering and whimpering in fear of what lay beyond in the next realm. Therefore, even if he had been able to successfully obtain the Elder Wand from its previous owner, he would never have been able to master it.
The Elder Wand by Dana Huff at The Pensieve: An Academic Guide to Harry Potter.
And from my comments below:
ES: (MuggleNet) “Ask Jo” contest winner Asrial, who’s 22, asks, “If Voldemort saw a boggart, what would it be?”
JKR: "Voldemort's fear is death, ignominious death. I mean, he regards death itself as ignominious. He thinks that it's a shameful human weakness, as you know. His worst fear is death, but how would a boggart show that? I'm not too sure. I did think about that because I knew you were going to ask me that."
ES: A corpse?"
JKR: "That was my conclusion, that he would see himself dead."
Mugglenet and The Leaky Cauldron JK Rowling Interview July 16, 2005
The other consideration is the fact that a conquered wand does not always bend its will to its new owner: the wand chooses the wizard. Ollivander says the conquered wand will usually bend its will, but it's dependent upon a lot of factors, including the manner in which it is taken. Instead of quoting a whole page of text, I'm going to refer to Deathly Hallows, chapter 24, The Wandmaker, (page 399 British Hardcover; page 403 US Hardcover), starting with This was the wand of Draco Malfoy and going to I think so. Subtle laws govern wand ownership, but the conquered wand will usually bend its will to its new master.
Ollivander explains something that I found interesting. "An initial attraction, and then a mutual quest for experience, the wand learning from the wizard, the wizard from the wand." Deathly Hallows - Pages 399/403 respectively.
I don't believe that Voldemort would have deigned to consider that he might have anything to learn from a wand, an object. Dumbledore explained how Voldemort was ultimately a fairly ignorant wizard.
‘And his knowledge remained woefully incomplete, Harry! That which Voldemort does not value, he takes no trouble to comprehend. Of house-elves and children’s tales, of love, loyalty and innocence, Voldemort knows and understands nothing. Nothing. That they all have a power beyond his own, a power beyond the reach of any magic, is a truth he has never grasped.' Albus Dumbledore - Deathly Hallows - Page 568 - British Hardcover (709 - 710 US Hardcover)
Without the reciprocity of the wand learning from the wizard and the wizard learning from the wand, combined with Voldemort's inability to face death and his dismissal of anything he does not deem valuable (which indeed is very valuable and powerful), I can't see how he could master the Elder Wand under any circumstances. How the wand is taken is but one factor in a very complex equation of wandlore and the assignment of wand allegiance.
