NO. Because Voldemort doesn't understand Wandlore at all.
It is evident from book 4 through 7 that there are "certain kinds of magic" of which Voldemort had no knowledge. In the graveyard when his wand failed to kill Harry he didn't know why and he didn't even question that till much later. Then in the end of Order of Phoenix when he failed to possess Harry physically, he just couldn't fathom that there might be something about Harry which makes him superior to him. Voldemort's biggest mistake was his vanity. Dumbledore says this himself
“And his knowledge remained woefully incomplete, Harry! That which
Volde- mort does not value, he takes no trouble to comprehend. Of
children’s tales, of love, loyalty, and innocence, Voldemort knows and
under- stands 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.
Deathly Hallows: Chapter 35: Kings Cross
Only when he went after Harry at the beginning of Deathly Hallows, he borrowed Lucius's wand (As Ollivander told him under torture) and when it failed again, instead of understanding the problem he naturally tried to look for another solution. When he found out about existence of "the most powerful wand" his natural desire was to possess it without understanding how its ownership truly works. I don't think he even knew the concept of Elder Wand's power being destroyed if its owner died undefeated. Voldemort understands only power and to him murder meant the ultimate power over the enemy. So he made sure to murder all the living people who had previously possessed Elder Wand (Gregorovitch, Grindelwald, Snape).
Also, voldemort does realize that the wand is still not working for him properly but he misunderstands it and kills Snape thinking that it was because of Snape that the wand refused to be truly his.
“I have a problem, Severus,” said Voldemort softly. “My Lord?” said
Voldemort raised the Elder Wand, holding it as delicately and
precisely as a conductor’s baton.
“Why doesn’t it work for me, Severus?”
“My—my lord?” said Snape blankly. “I do not understand. You—you have
performed extraordinary magic with that wand.”
“No,” said Voldemort. “I have performed my usual magic. I am
extraordi- nary, but this wand. . . no. It has not revealed the
wonders it has promised. I
feel no difference between this wand and the one I procured from
Ollivander all those years ago.”
“Why did both the wands I have used fail when directed at Harry Potter?”
“My wand of yew did everything of which I asked it, Severus, except to
kill Harry Potter. Twice it failed. Ollivander told me under torture
of the twin cores, told me to take another’s wand. I did so, but
Lucius’s wand shattered upon meeting Potter’s.”
“I sought a third wand, Severus. the Elder Wand, the Wand of Destiny,
the Deathstick. I took it from its previous master. I took it from
the grave of Albus Dumbledore.”
“All this long night when I am on the brink of victory, I have sat
here,” said Voldemort, his voice barely louder than a whisper,
“wondering, wondering, why the Elder Wand refuses to be what it ought
to be, refuses to perform as legend says it must perform for its
rightful owner. . . and I think I have the answer.”
“The Elder Wand cannot serve me properly, Severus, because I am not
its true master. The Elder Wand belongs to the wizard who killed its
last owner. You killed Albus Dumbledore. While you live, Severus, the
Elder Wand cannot truly be mine.”
Deathly Hallows: Chapter 32: The Elder Wand
This clearly indicates that Voldemort was alerted in some way that the wand didn't truly belong to him. Even when Harry tells him that Snape did not truly defeat Dumbledore since they had planned the death in advance, he failed to understand what it meant or wand might not have power since its last owner was undefeated.
“That wand still isn’t working properly for you because you murdered
the wrong person. Severus Snape was never the true master of the Elder
Wand. He never defeated Dumbledore.”
“Aren’t you listening? Snape never beat Dumbledore! Dumbledore’s death
was planned between them! Dumbledore intended to die undefeated, the
wand’s last true master!
“But then, Potter, Dumbledore as good as gave me the wand!”
Voldemort’s voice shook with malicious pleasure. “I stole the wand
from its last master’s tomb! I removed it against its last master’s
wishes! It’s power is mine!”
Deathly Hallows: Chapter 36: The flaw in the Plan
And lastly I think the power of Elder wand will die if the last owner is undefeated and this is confirmed by conversation between Harry and Dumbledore.
“I’m putting the Elder Wand,” he told Dumbledore, who was watching him
with enormous affection and admiration, “back where it came from. It
can stay there. If I die a natural death like Ignotus, its power will
be broken, won’t it? The previous master will never have been
defeated. That’ll be the end of it.” Dumbledore nodded. They smiled at
Deathly Hallows: Chapter 36: The flaw in the Plan