In the last book, Voldemort kills Harry with the Killing Curse. Minutes before though, he had Nagini kill Snape to gain the allegiance of the Elder Wand (which means, the kill has to be done by himself, I guess it technically counts because Nagini is a Horcrux (?), but that's not the question).

Now imagine Harry meeting Voldemort in the Forbidden Forest, and Voldemort instead of using the Killing Curse again commands Nagini to bite Harry to death. First of all, it would have been a slower death (begging the question: at which point would Dumbledore show up in his head?), but also the body would be left behind destroyed to a point where it is unfit to contain any life. So would Harry have been able to return to the living, if killed by Nagini and therefore dying due to e.g. blood loss/poison?

The only way for this plan (Dumbledore's, I guess) to be fool-proof requires Harry to be invulnerable to Nagini, is that correct or did I miss something?

Edit: I agree that the likelihood of Voldemort using the Killing Curse approaches 1, since he is very proud and has to prove he can do what he previously failed, to overcome the shame of failing or whatever, I just wondered what would have happened if he had been smarter. In fact, this inspired a whole different question which I might ask later if my research will end up without results ;)

Nagini probably could have killed Harry.

The protection Harry had from his mother’s sacrifice only was from harm directly done by the Dark Lord, not from anyone or anything working for him, or from the Horcruxes. Therefore, there’s no reason to think Nagini couldn’t kill Harry - he’s clearly not made immune to venom of serpents controlled in some way by the Dark Lord since the basilisk, directed by his Horcrux, nearly killed Harry until Fawkes saved him with phoenix tears.

“But as warm blood drenched Harry’s arms, he felt a searing pain just above his elbow. One long, poisonous fang was sinking deeper and deeper into his arm and it splintered as the basilisk keeled over sideways and fell, twitching, to the floor.

Harry slid down the wall. He gripped the fang that was spreading poison through his body and wrenched it out of his arm. But he knew it was too late. White-hot pain was spreading slowly and steadily from the wound. Even as he dropped the fang and watched his own blood soaking his robes, his vision went foggy. The Chamber was dissolving in a whirl of dull colour.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 17 (The Heir of Slytherin)}}

Harry was protected by his mother’s sacrifice since the Dark Lord tried to kill him, but it had no effect on the basilisk venom. The basilisk was controlled by one of the Horcruxes, and Harry was still susceptible to its venom. With this in mind, there’s no reason to think it wouldn’t be possible for Nagini to kill him. This would remain the same after the Dark Lord rebuilt his body with Harry’s blood. That helped Harry because the Dark Lord kept Lily’s sacrifice and the protection it provides alive in his body.

“He took your blood believing it would strengthen him. He took into his body a tiny part of the enchantment your mother laid upon you when she died for you. His body keeps her sacrifice alive, and while that enchantment survives, so do you and so does Voldemort’s one last hope for himself.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)}}

It kept alive the protection that the sacrifice gave Harry, but that protection only worked against the Dark Lord himself, not those he commands. It wouldn’t protect Harry from Nagini, like it didn’t protect him from the basilisk years earlier.

But the Dark Lord wanted to do it himself.

While it’s likely Nagini could’ve killed Harry, the Dark Lord very much wanted to kill Harry himself. He wouldn’t want Nagini to.

“I have been careless, and so have been thwarted by luck and chance, those wreckers of all but the best laid plans. But I know better now. I understand those things that I did not understand before. I must be the one to kill Harry Potter, and I shall be.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 1 (The Dark Lord Ascending)}}

The Dark Lord would likely consider letting Nagini do it as not doing it himself, since he’d want Harry to die at his own hand directly to show his own superiority. He wanted to fight Harry, allow Harry to fight back, and be proven stronger by his victory.

“You see, I think, how foolish it was to suppose that this boy could ever have been stronger than me,’ said Voldemort. ‘But I want there to be no mistake in anybody’s mind. Harry Potter escaped me by a lucky chance. And I am now going to prove my power by killing him, here and now, in front of you all, when there is no Dumbledore to help him, and no mother to die for him. I will give him his chance. He will be allowed to fight, and you will be left in no doubt which of us is the stronger.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

Letting Nagini kill Harry wouldn’t seem sufficient to him as a way of clearly proving that he could defeat Harry himself.

There was clearly some sort of magic at work, probably of a similar type to the charm of Harry's mother's protection, that played a role in Harry's death/non-death, so it seems unclear to me what would have happened if he had died/not-died from physical trauma. Perhaps he would have healed magically, for instance.

However, Dumbledore had studied very closely Voldemort's character. I think he was pretty certain that Voldemort would try to kill Harry using the killing curse. Since Harry was his particular enemy, and he wanted to indisputably demonstrate to everyone that he was Harry's superior, it seemed likely he would want to execute him by his own hands, rather than even through Nagini, and that if so, those he dispatched by his own hands were always executed using Avadra Kedavra.