the exhaust carries hot air away.. if you cannot do that, it won't cool the room. more heat is generated than removed. so it'll only warm the area in an extremely inefficient way, but would still act like a space heater, lol.
got a window? buy the little attachments for ac exhaust (can make one easy enough with a slat of wood, hole saw and a appriately sized fitting for exhaust duct) or create a switch for your luandry exhuast when not in use...
so if you cannot pipe the hot air elsewhere and isolated from that room, it will only warm it up.