I know and have mentioned the shop no longer being available for that run in the comments section - however, the first time you encounter the Payday items during a run you more often than not won't have the items that allow you to steal which is the reason for using this method.
Yeah, it works with all of the Payday 2 items if you're unequiped to steal them. Haven't had the Loot Bag yet - just the Drill and the Clown Mask so far.