Can bromide ion ever act like a base?
Come on, you can figure out this one on your own! How do you compare acidities? Here's a helpful hint.

Armed with that information, I have to add something. I believe the mechanism as drawn above is not universal: it sure depends on the conditions and solvent used. Some other proposed mechanisms involve the enol, rather than the protonated ketone, which might be more plausible in mild conditions. In water, anyway, HBr is fully dissociated and it shouldn't be “reformed” like that. The proton will return to be solvated in the solution.