Are crowned teeth more likly to have abcsesses than teeth that have had no cavities?

Yes they are. First of all, teeth that need crowns have either 1) had a lot of or deep decay 2) been traumtized in an accident or been broken off accidently. The decay or trauma causes an inflammation to the nerve, which then can cause the tooth to die or an infection that results in an abcess. (It is like hitting your thumb with a hammer - it gets red and throbs because blood rushes to the injury. The same happens to a tooth, but the bloodflow is so much less that it stays in the nerve canal and kinds of cuts off the good blood flow) Sometimes if a crown is placed on a tooth simply for cosmetic reasons, the preparation of the tooth by drilling can cause enough trauma to cause the nerve to die.