Has anyone ever heard of the myth of a man who escaped his execution a long time ago by inserting a metal tube down his throat so that he could hang yet still breath?
No even if your airway remains open the rope will still cut off vital blood circulation to the brain...that's if your neck isn't broken. A proper hanging causes death not by strangulation but by breaking the condemned person's neck.
EDIT: Something else to think about there's no way you can put a rigid tube down someone's throat without them gagging on it. Even in a medical situation with trained personal using flexible tubing it's a tricky procedure.