I can't imagine season 3 Faith as a non-headcase so I have a hard time imagining it. But she did show some good qualities back then, and we've seen more of them now, specially in season 8 & 9, so maybe if some things had turned out differently it could have worked.
Here's a scenario:
Buffy tries to live a normal life(maybe she's been injured and needs months to heal) and Faith trying to be the one and only slayer, having help from Giles, Willow and the others. It would be weird, considering she's a loner who's not used to giving orders and getting help from other people (other than her watcher). It would probably have worked badly, so we could see the consequences of that. Willow & Oz & Cordy & Xander & Giles trying to help, Faith not being able to handle getting help or leading them and giving them the cold shoulder, Buffy trying to live a normal life but in the end, she misses slaying but doesn't want to steal Faith's thunder. Faith turns out not being able to handle the pressure being the one and only slayer, and the scooby gang trying to be supportive and tells Buffy they're doing okay without her, which is a lie. Buffy wants to return, the others want that too, but they're all too nice or afraid to ask her.
If TV seasons were longer, maybe this arc could have been put in in season 3, pre-Evil Faith.