I think Avon's attitude to any kid of his would depend a lot on the circumstances surrounding it. If he *had* slept with Cally then I'm certain he would feel responsible for the kid and do his best (which may not be that great - he's hardly the parental type). If he feels responsible for something he does act to do something about it whether it's what he'd prefer to do or not.
However if the kid was produced as a result of an outside force interefering I could see him denying any responsibilty for it and having nothing to do with it. He did nothing to create the situatation - not his problem sort of attitude.
Leia