I have been pondering this question of late. From the information that JK Rowling has given us from the Harry Potter books, what is expected to happen (or not) if someone other than Voldemort had cast Avada Kedavra on Harry (while Harry was still a Horcrux)?
There are several aspects to be considered before answering this question. Firstly, Harry’s body does not contain only his soul but also Voldemort’s, i.e. Harry Potter = Harry Potter’s body + Harry Potter’s complete soul + Voldemort’s one-eighth soul.
Next, Avada Kedavra seems (http://scifi.stackexchange.com/questions/65638/what-type-of-damage-does-avada-kedavra-do) to make the body on which it is cast lifeless and separates the soul from the body (in a single-souled body). Therefore, assuming that Avada Kedavra can make the body lifeless, which soul(s), if any, would an Avada Kedavra separate from Harry’s body? Would souls have the choice of their fate? To move on or be a ghost maybe. (As an aside, are the talking portraits some form of a ‘Horcrux’?)
But then, Harry is a Horcrux, that is, he’s a container for Voldemort’s soul. Applying the rule for destruction of Horcruxes, he cannot be destroyed simply by Avada Kedavra. However, which part of ‘Harry’ is the container for Voldemort’s soul? Is it Harry’s body only? If it’s Harry’s body only, then the Avada Kedavra should not be able to have the usual effect it would have on a body of making it lifeless (which can be thought of as rendering the container incapable of holding a soul). If it’s not Harry’s body only but also his soul, then, well, the container (= Harry’s body + soul) cannot also be destroyed by Avada Kedavra. Therefore, the Avada Kedavra is not expected to produce the effect of making Harry’s body lifeless when it is cast by someone other than Voldemort. Consequently, Voldemort’s one-eighth soul cannot be destroyed by casting Avada Kedavra on Harry.
Finally, Harry’s blood runs in Voldemort’s body as well – which is a sort of Harry’s Horcrux, so Harry cannot die. Therefore, Avada Kedavra, if was cast by someone other than Voldemort, even if it manages to separate his soul from his body, since his body cannot be made lifeless, could he have just flipped back to his body?
What exactly happened when Voldemort cast Avada Kedavra on Harry in the forest? Harry’s body, I think, couldn’t be made lifeless since it was the Horcrux-container. However, both souls split from the body. And Harry and Voldemort respectively went into the ‘after-life/limbo’ zone since each of their souls was split from Harry’s body. Harry’s soul chose to come back to his body. Could Voldemort’s one-eighth have also chosen to come back to Harry’s body or some other object? Was Voldemort afraid of the limbo zone and chose not to bring that part of his soul back?
In any case, it would have added more drama and intrigue to the story and to the aura of The Chosen One if someone had tried to cast the Avada Kedavra on Harry and it failed to kill him or had produced some unusual effect.