I think she could have. Despite everything that happened to her, I genuinely don't think that Faith is a bad person. I think she has/had some major demons she needs to work out and that coupled with superpowers is obviously a terrible mix. However, Angel seemed to be winning her over before Wesley barged in. That being said though, like others have mentioned, she hadn't totally hit rock bottom yet.
I really do think that towards the end of S1, she wouldn't have found her way back without Angel. He completely saved her. Without him, Buffy would have beat the hell out of her again and probably killed her. Angel knew that was almost what Faith wanted, and he saved her.