When bleeding to death, people never really experience it at all, they pass out first. There is some evidence that people are aware some 15-30 seconds after beheading. So if chickens are like people, there's your answer. If they aren't, then no one knows but most will say "instantly!."
The involuntary movement after death happens either way. Yes, it's not fun to watch. So I don't. I use kill cones and turn my back when they begin that. Yeah, I'm a wimp but I still get 'er done.