Pretty sure it does. One of the software's main cron entries, the daily clean up, runs daily at 3 am (so 0 minutes). That's a cron that we'd know wasn't running if it wasn't running.
So I've gone into developer mode and edited the cron entry for "User group promotions" and set the "Run at minutes" for 0, 20 and 40. 20 and 40 seems to execute fine but 0 does not. Meaning at 0 the user does not promote automatically.
