They survive in this edit. Afterwards, Amy has a chat with the Doctor, then decides it's better to spare the Doctor from watching them "fade from him" so she writes him a goodbye note telling him he'll never see them again, which creates a fixed point for him, which is in-keeping with the episode thematically ("once you know what's coming, it's written in stone"). Anything's better than "I can't stop by Manhattan in a sodding time machine because reasons"