While not ideal, even on unfamiliar (but decent) gear, it should be possible to get workable tones and set reasonable volume in under a minute.
The drummer should recognize he's too loud, and he should adjust. If he can't listen and he can't vary his volume, that's not a problem sound check will fix.
Getting ideal guitar tones on unfamiliar gear is hard, but getting to a reasonable clean tone, setting *roughly* the right amount of distortion, and getting volume in the ballpark should be quick. Bass is more or less the same story: you should be able to get a pretty good ballpark tone even on unfamiliar gear in about a minute.
This all hinges on musicians knowing what they're doing. Unfortunately most don't.
I do gigs with no sound check from time to time. With my own rig it's a piece of cake... my setup is practically incompetent soundman-proof. Using someone else's rig is usually a matter of not using drastic tweaks at the amp and controlling the rest from my bass with my hands and/or EQ. Get a good clean tone at the max volume you'll probably need and you should be fine.
Then if everyone LISTENS and PLAYS WITH EACH OTHER TO THE CONSTRAINTS OF THE VENUE things usually work out fine.
So yeah, it can be done.