closet air-conditioning unit?

I'm in the process of purchasing a prewar co-op that has a small 1/2 bathroom (no longer being used as such), but which still has intake/waste water lines and a narrow window (probably 6" wide). I'm wondering if a room like this, essentially a 2' x 4' closet, can accommodate an air-conditioning unit that doesn't require any exterior condenser/unit. The building doesn't allow for wall-thru units or anything requiring an exterior unit like a mini-split. This closet shares a wall with the kitchen and the dining room, and even if those are the only two rooms this sort of system can service, it may be worth the trouble. Obviously this is all subject to co-op board approval, but I wanted to see if this is even mechanically feasible.