Not really. If my school produced murderers, we'd definitely know about it. It would be a big deal. Like certain notorious schools in inner city London.
There were some crazy nut cases in my comprehensive school in the north of England, but even they seemed to have eventually lived fairly decent lives.
Having been to university with a large number of old Etonians, I can tell you with some confidene that a significant proportion of them believe themselves to be above the law.
And sadly that belief is entirely rational and supported by the facts, the British legal system being designed with the overriding concern of protecting the aristocracy and Establishment.