Only if the black belt knows that the other is a white belt. If the black belt assumes the other has the same experience as him/her than all bets are off.
Which has, of course, been the real reason for belt ranking from the beginning, and points to some of the reasons for the original post: if two black belts in system X face off, and one of them is....I dunno....me: 6'2", 230 lbs., and once called by one sensei, "Positively homicidal." (this was, of course, before the subway incident...) against a 7, no make that a 12 year old black belt: 5'5", 100 lbs., are "all bets off?"