It does add to Johnny's character. He obviously loves her but also considers her hopeless, but he considers himself hopeless too. He's fair to her but he's not going to try to be happy with her anymore. He can't get rid of her either. If she's in serious trouble he'll still rescue her. Like the Lost, she's something Johnny got into that he's never going to get out of completely.
I didn't like Ashley - the missions you have to do for her actually turned me off of Johnny's character as a whole. I mean here you are playing as this tough biker and you're running around doing missions in order to save a drug addicted whore. In fact I wish we would have had an option to kill her after Jim is murdered.