@Keru Only played uscf a bit in high school. I would hope that if black just lets his clock flag an arbiter would have the option of determining whether checkmate is possible with the position and ruling the game a win for white.
:after 15 minutes of reading the rulebook, I haven't come to this exact scenario, but from a few similar things the arbiter has a lot of authority on declaring a draw or win in positions like these. Obviously white would claim a win, and I think the arbiter would agree therefore it's likely a win under uscf rules. (unless there's something else in the rulebook that counters this)
This is also why a bishop with no real mating chances is declared a draw, because there is no reasonable way checkmate can be achieved (this turns those earlier positions where pawns exist but no real chance of winning into potential draws, but I don't think that would actually be the case)