No, I work in a maximum security prison and there are people there who Conor would shit his pants around, and rightly so. If you think his skills automatically translate into winning every prison fight then you're extremely misinformed. As for how many killers kill grown men with their bare hands: more than you think, and just because they used a weapon doesn't mean they had to, and doesn't mean they won't against him. Conor would be a trophy punk and prospecting for the first group that would take him. He would be exploited for his money, his fame, and end up fighting for people he doesn't even like, against people he has no personal beef with, for someone else's profit. His best chance of survival would be to start hanging with a gang and teach the lessor members aspects of fighting to pay his way through. At that point they'd probably throw him in segregation which is what he'd want to begin with.
As for them being scared, they aren't scared to be shot, they're not going to be scared of Conor, and if by any means he did kick someone's ass, he'd be wise to be scared for his life until he left that place.