Yes, Harry would have survived, and so would Voldemort.
The specific sequence of events was as follows:
Voldemort shoots Avada at Harry in the forest.
Voldemort's Avada severes/destroys the piece of V's soul attached to Harry.
However, it did NOT bounce back on him unlike 19 years ago, and does nothing to his own remaint of soul or his body!
(remember that what happened the first time he tried to kill Harry, was that his Avada which bounced off of Harry destroyed his body! This didn't happen this time)
Harry is NOT killed by Avada because he is protected by Lily's protection which still flows through Voldemort's veins due to taking Harry's blood.
And since Voldemort's body is still alive, that blood still protects Harry.
The important part is that that - since the Avada did NOT bounce back and kill him - the presence or absence of Horcruxes was irrelevant to what happened.
What the Horcruxes do in general, and did for him originally, 19 years ago, was keeping his soul alive after the Avada Kedavra (which bounced off of Harry) killed his own body. Since this didn't happen in the forest, the Horcruxes were not needed.
Horcruxes don't revive people from fainting.