Voldemort would've been able to repair his soul. Assuming he's capable of feeling remorse. Or willing to.
When Hermione discusses Horcruxes with Harry and Ron, she mentions there's a way to repair your soul, by feeling authentic remorse.
However, she doesn't mention anything about not being able to repair your soul if an Horcrux was already destroyed. Considering that at that point the Diary and the Ring were already destroyed, Hermione would've probably made a comment about it not being possible for Voldemort, if that were the case.
Harry remembered what Dumbledore had said about Voldemort moving beyond “usual evil.”
“Isn’t there any way of putting yourself back together?” Ron asked.
“Yes,” said Hermione with a hollow smile, “but it would be excruciatingly painful.”
“Why? How do you do it?” asked Harry.
“Remorse,” said Hermione. “You’ve got to really feel what you’ve done. There’s a footnote. Apparently the pain of it can destroy you. I can’t see Voldemort attempting it somehow, can you?”
Harry Potter and the Deathly Hallows. Chapter Six. The Ghoul in Pajamas
Considering the book she's consulting mentions the method to restore the soul, it would very likely mention any possible limitation on restoring the soul, and Hermione would've made a comment about that.
Harry certainly thinks it is possible, and Voldemort doesn't retort to him that it wouldn't be possible due to the destroyed Horcruxes.
“You’re right. But before you try to kill me, I’d advise you to think about what you’ve done... Think, and try for some remorse, Riddle...”
Harry Potter and the Deathly Hallows. Chapter Thirty-six. The Flaw in the Plan.
I casually found further evidence that supports Voldemort being able to restore his soul. Apparently Voldemort was capable of healing "more deeply than anyone would have supposed" if he had repented, which in my opinion hints to him being able to remorse his soul back... However, it seems it's thanks to Lily's blood?
except that the power of Lily's sacrifice is a positive force that not only continues to tether Harry to life, but gives Voldemort himself one last chance ... Voldemort has unwittingly put a few drops of goodness back inside himself; if he had repented, he could have been healed more deeply than anyone would have supposed.
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