How well could Aegon IV have done as a king, if he was just as much of a womanizer and father of bastards, but otherwise a competent king?

Pretty damn well. After all, Garth the Greenhand outdid Aegon IV when it came to sleeping with every woman he could, and he’s revered in the Reach. As long as the King is good at their job/lucky enough to be ruling in a prosperous and peaceful time, the epic-manwhoring feeds into the whole Fisher King/fertility god thing and the people will think you’re a virile, merry king who’s responsible for the good times. 

It’s when you fuck up or things go badly that they start to say you only think with your balls.