It'll depend on the noose... if it's made of cheesewire then you'v got no chance.
And anyway, since when have people who have been in prison awaiting a death sentence ever been really healthy?
I dont think even then, was watching mythbusters and there was an episode testing if a cable when snapped could cut flesh. I don't remember the strengths they tested but the results were the same, it just left a huge mark.
Well there's a slight difference in getting hit with a cable and having a thin but strong wire tighten around your neck. I'm pretty sure if a thin, strong wire were used to hang someone, they would probably get decapitated, or at least they would be cut down to the bone and then hang by the bone.