I don't think he's likely to trade down. Not that he won't, but looking at the current 53-man projected roster, there aren't seven obvious holes. Let alone 8, 9, or 10 with added capital.
Rather than draft nine guys and have to release both of our 7th rounders, hoping they make it to the practice squad, just because of space, I'd prefer to draft five, have them all make the roster, and have the best player on Brad's board (when he moves up) make a significant impact on day one.