This sounds like a great idea, but one that can get tricky to delineate.
Cheengs, Screege, snowglobe, the xiblaxian holo-wrist-putters, the camp scout backpack and the mayflower bouquet are the ones that will drop items just for fighting arbitrary combats with them, I think. (I'm probably forgetting something, this list kept growing while I was typing up the rest of the post.)
Conditionally:
Crown of Thrones and Buddy Bjorn can do so too, assuming you put in the right familiars (which would really helpful if they were included, especially if it also extends to configurations that drop meat, then it would just suggest the misshapen animal skeleton when I want familiar weight instead of defaulting to the ghost pickle and forcing me to check the wiki page).
The Pantogram pants can drop items if you sacrifice a clover for the hilarity enchantment.
The Protonic accelerator pack will give you one of those psychokinetic blobs from any ghost you fight, whether you blast it or not.
Then there's a whole bunch of items that can give you additional combat drops, if you do 'something' specific to them during the combat, such as mayfly bait and pantsgiving.
Speaking of which, there's also equips that give other, tangible benefits for wearing them into combat, even if it's not dropping items, such as pantsgiving (again), any of the stinky cheese equips and the mafia thumb ring.