This would drive me as well as most people nuts. When the alarm sounds, if you don't get those pieces in the puzzle, it won't shut up. If that doesn't get you up (and all riled up!), I don't know what will.
This doesn't sound too fun if you had a long night. The pieces pop out when it goes off and will not stop until they're all back in their spot. I guarantee you AND your roommate will be wide awake by the time you finish.