No they don't.
There's plenty of child molesters living happily in jail. They get along just fine.
This explains why the Megan's Law website in your area doesn't show a map of little tombstones where child molesters used to live before they were convicted and sent to prison to meet their deaths as you imagine, but instead currently live after being released from prison.
The inmate population tends to beat the heck out of them. So yes, they do. Especially when they are found out.
Ever see “Kinjite”?