Theoretically, the original Sacrificial Protection would've been enough to shield Harry from that specific Killing Curse -the one cast by Voldemort in the Forbidden Forest-. That protection never faded, and was still active in Harry's blood.
When Voldemort cast the Killing Curse in the Forbidden Forest, it didn't work -again- due to Lily's original protection. But apparently, the Killing Curse is so powerful that it has some effect, even with the Sacrificial Protection, thus destroying Voldemort's soul inside Harry and sending him to the "limbo".
- Did Harry die?
Rowling wrote this very carefully, so it could be read two ways. "Did he just go into a state of unconsciousness in which his subconscious tells him everything he needs to know? Dumbledore doesn't tell him anything he couldn't have figured out with some educated guesses." But in her mind, Harry entered a limbo between life and death, and faced a choice about which way to go.
She explains on her website that this encounter involves some very deep laws of magic, which Voldemort himself did not understand: "Having taken Harry's blood into himself, Voldemort is keeping alive Lily's protective power over Harry — 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. But of course, he refused to feel remorse." Also, since Voldemort is using the Elder wand, which actually belongs to Harry, neither the Cruciatus or the killing curse work properly. "The Avada Kedavra curse, however, is so powerful that it does hurt Harry, and also succeeds in killing the part of him that is not truly him, in other words, the fragment of Voldemort's own soul that is still clinging to his. The curse also disables Harry severely enough that he could have succumbed to death if he had chosen that path."
About Voldemort taking the blood... When Voldemort took onto him Harry's blood, he also took onto him the Lily's sacrifice. Thus, he tethered Harry to life as long as Voldemort was alive. He acted as a sort of Horcrux for Harry, allowing him to come back if Harry somehow was about to die or close to death.
‘Precisely!’ said Dumbledore. ‘He took your blood and rebuilt his living body with it! Your blood in his veins, Harry, Lily’s protection inside both of you! He tethered you to life while he lives!’
Rowling, J.K.. Harry Potter and the Deathly Hallows (p. 579). Pottermore Publishing. Edición de Kindle.
It is a bit confusing, to be fair, but it seems that the original Sacrificial Protection shielded Harry to some exent, but the Killing Curse is so powerful that it sent him to the limbo, and because Voldemort still had Lily's protection in his blood, Harry was able to come back to life.