I've left 2 perfectly good Function / Tribute bands in the past due to "musical integrity" I've thought it would be good to get with a band that was doing decent original songs, but fact of the matter is, that more often than not, you still end up in bands that are playing music that your still not really into playing because of the lack of vacancies, at least in Derbys, Notts area.
I can't play classic rock anymore because its not challenging enough, so to go back to the original post, I would learn the tunes because if nothing else you might learn one or two new licks.
For the most part Muso's are to**ers, and trying to get in a band that is stable enough without at least one band member threatening to leave every other gig is very hard.