How were the Horcruxes affected when Voldemort failed to kill baby Harry?

Question

After Voldemort fails to kill Harry when Harry is a baby, the Avada Kedavra Curse rendered him a spectre-like being.

In Goblet of Fire, Voldemort says:

I was less than spirit, less than the meanest ghost ... but still, I was alive. What I was, even I do not know ... I, who have gone further than anybody along the path that leads to immortality. You know my goal – to conquer death. And now, I was tested, and it appeared that one or more of my experiments had worked ... for I had not been killed, though the curse should have done it.

_{Goblet of Fire - page 566 - Bloomsbury - chapter thirty-three, The Death Eaters - Voldemort}

and:

‘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. I set my sights lower ... I would settle for my old body back again, and my old strength.

_{Goblet of Fire - page 569 - Bloomsbury - chapter thirty-three, The Death Eaters - Voldemort}

Voldemort says he was willing to embrace mortal life again before chasing immortality.

Does this mean that when Voldemort was in his spectre-like, less-than-a-ghost state, the Horcruxes were somehow not keeping him immortal? Voldemort himself describes himself as being in a state where he had to embrace mortality again before pursuing immortality. What does this mean?

ETA: To clarify, a different way to ask this question is: How could Voldemort have "embraced a mortal life" while he had Horcruxes -- didn't the Horcruxes make him immortal?

I really have no opinion one way or the other -- I'd like to consider all interpretations (please keep them based in canon.)

Answer 1

I believe the Horcruxes acted as they're supposed to between Voldemort failing to kill Harry as a baby and him regaining even a rudimentary body. The pieces of his soul that had been encased in objects bound the rest of it to the earth, preventing him from being truly killed and making him functionally immortal while they remained intact. Nobody seems to know exactly what Voldemort was during that time, so I'm not sure how anybody would have gone about killing him anyway, other than by destroying the Horcruxes he'd made and hidden already.

His initial plan was to steal the Philosopher's Stone and use the Elixir of Life to regain a new body, at which point he'd have no use for anything but his Horcruxes. He would be as powerful as he had been immediately prior to being destroyed in Godric's Hollow, and would then only require his Horcruxes to keep him alive. Dumbledore explains this to Harry during one of their many lessons in his sixth year:

I believe that he would have found the thought of being dependent, even on the Elixir, intolerable. 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. Thereafter, I am convinced, he intended to continue to rely on his Horcruxes. He would need nothing more, if only he could regain a human form. He was already immortal, you see… or as close to immortal as any man can be.
_{Harry Potter and the Half-Blood Prince, Chapter Twenty-Three - Horcruxes}

I think that when he refers to "mortal life" he means the frail body he possessed prior to the events at the end of Goblet of Fire when he regained his new body. At that point he was incapable of surviving on his own, and was entirely dependent on Wormtail's care:

“Your devotion is nothing more than cowardice. You would not be here if you had anywhere else to go. How am I to survive without you, when I need feeding every few hours? Who is to milk Nagini?”

“But you seem so much stronger, My Lord —”

“Liar,” breathed the second voice. “I am no stronger, and a few days alone would be enough to rob me of the little health I have regained under your clumsy care. Silence!”

Not truly mortal, since he still had his Horcruxes to anchor his soul to the living world, but he was at great risk of sliding backwards to the part-life state he was in previously. He was weak and completely helpless, which is precisely how I imagine Voldemort saw most (if not all) people who were actually mortal, and wouldn't be a preferable state for him.

Answer 2

Since you are asking for interpretations that do not go against canon, my interpretation is that Voldemort had not really reached the immortal state that he wanted to reach yet, and horcruxes were only the first part of his plans. He probably had future plans after creating the required number of horcruxes, but he was thwarted before that could happen, when he attacked Harry. At the point when he had attacked him, he was still short of having a seven part soul, and, as I mentioned, that was only the first part of his plans to obtain immortality

His encounter with Harry showed that, although he was powerful magically and could not actually be defeated completely until all his horcruxes are destroyed, his main body that held the main part of his sentience was still destructible, and destroying the body could leave him in a completely vulnerable state. His ultimate goal was probably to exist in a form that was indestructible

As for how were the horcruxes affected when Voldemort failed, from the books we know that they weren't affected in any way at all. Dumbledore was able to find all of them as they were when Voldemort had left them at their respective places (except for the locket I guess), and the part of him in the diary did not even know the "main" Voldemort was destroyed until Ginny told him about it