That is amazing.
Best we had was some idiot who thought he could get away with smoking in the bathroom like the jocks in an 80's movie... Someone walked in, and he threw his cigarette butt in the trash can, where it started to smolder.
A lot.
All told, it was a pretty boring fire. No real damage, but the school was closed for a couple of days while they cleaned up the soot.
It sounds like you're probably good.
The slope itself shouldn't matter as long as the drain hole at the bottom of the sink is still higher than the drain hole in the wall. You can also angle the p-trap itself a little bit, but it still needs to be able to hold enough water in the bottom to block the pipe.