Absolutely, Voldemort destroyed the Horcrux, and Harry survived, because he had all 3 of the Hallows and was therefore "Master of Death"I also think these movies were poorly named. I don't know how different the books are, but these movies had very little to do with the Deathly Hallows. They kept foreshadowing that whoever possesses all three Hallows becomes a Master of Death...and then nobody ever possesses them! The Resurrection Stone didn't even serve a purpose except to allow Harry's dead relatives to give him a pep talk.
Well, the way I interpreted this in the books (and maybe I'm wrong) is that Harry did indeed possess all of the Hallows (even though he didn't physically hold the Elder Wand until the end he was still its rightful owner), and that because he had all three of them and was Master of Death, that is why he did not die when Voldemort used the Avada Kedavra curse on him in the woods. The curse killed the Voldemort part inside of Harry but left Harry intact because he was the Master of Death. The only other explanation for him coming back to life is that because Voldemort was using the Elder Wand to cast the curse, it didn't affect Harry and instead rebounded to Voldemort, knocking him on the ground. But then why was it able to kill the bad part inside of Harry if it had rebounded? I feel like the Hallows did indeed play a large role because they brought Harry back to life.