Did Voldemort believe that the Elixir of Life could save him from the curse of drinking Unicorn blood?

Question

In Philosopher's Stone, Voldemort says:

"See what I have become?" the face said. "Mere shadow and vapour...I have form only when I can share another’s body...but there have always been those willing to let me into their hearts and minds...Unicorn blood has strengthened me, these past weeks...you saw faithful Quirrell drinking it for me in the forest...and once I have the Elixir of Life, I will be able to create a body of my own...Now...why don’t you give me that Stone in your pocket?"
_{(Philosopher's Stone, Chapter 17, The Man With Two Faces).}

Did he think that the Elixir of Life could remove the cursed life that drinking unicorn blood brings?

Answer 1

His action proved that he believed in it. There are details in the book which prove it.

“The ancient study of alchemy is concerned with making the Sorcerer’s Stone, a legendary substance with astonishing powers. The stone will transform any metal into pure gold. It also produces the Elixir of Life, which will make the drinker immortal.”

_{^{Harry Potter and the Sorcerer's Stone, Chapter 13, Nicholas Flamel}}

Firenze believes Elixir of Life will resolve the issue with the curse of drinking Unicorn blood

“But who’d be that desperate?” he wondered aloud. “If you’re going to be cursed forever, death’s better, isn’t it?”

“It is,” Firenze agreed, “unless all you need is to stay alive long enough to drink something else — something that will bring you back to full strength and power — something that will mean you can never die. Mr. Potter, do you know what is hidden in the school at this very moment?”

“The Sorcerer’s Stone! Of course — the Elixir of Life! But I don’t understand who —”

_{^{Harry Potter and the Sorcerer's Stone, Chapter 15, The Forbidden Forest}}

And finally Voldemort himself accepting it.

“you saw faithful Quirrell drinking it for me in the forest…and once I have the Elixir of Life, I will be able to create a body of my own….Now…why don’t you give me that Stone in your pocket?”

_{^{Harry Potter and the Sorcerer's Stone, Chapter 17, The Man With Two Faces}}

Answer 2

The Dark Lord knew it would give him a body and immortal life.

The Dark Lord didn’t seem particularly concerned about whether the Elixir of Life would remove the curse that killing a unicorn and drinking its blood carries, but he wanted the Philosopher’s Stone for two reasons - to assure himself immortal life and to regain a body.

“But my plan failed. I did not manage to steal the Philosopher’s Stone. I was not to be assured immortal life. I was thwarted … thwarted, once again, by Harry Potter …”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

Though the Dark Lord was willing to change his plan once he knew he couldn’t get the Stone, he’d wanted it to restore himself to a hopefully stronger body.

“There was no hope of stealing the Philosopher’s Stone any more, for I knew that Dumbledore would have seen to it that it was destroyed. But I was willing to embrace mortal life again, before chasing immortal.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

Also, Dumbledore said that the Dark Lord wanted it to regain a body, though he said the Dark Lord wouldn’t want to remain dependent on the Elixir of Life for too long.

“Of course he was prepared to drink it if it would take him out of the horrible part-life to which he was condemned after attacking you, but only to regain a body.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)}}

It’s made clear why the Dark Lord wanted the Philosopher’s Stone, but removing the unicorn blood curse didn’t seem to be anywhere among his considerations.