Fans work on humans by speeding up the evaporation of sweat - we sweat, it's warm, the air takes it away, so our skin is cooler. Doesn't really work for our furry friends!
Fans can be of some use but you need a cooler air source - a fan in an enclosed room will do nothing but circulate air of the same temperature. Infact, as hot air rises, bunnies are usually in the coolest part of the room anyway, so a fan will just blow their slightly cooler air around the room and warm it up with the warmer air getting mixed in.
If it's not cooler outside, you can cool the air yourself with ice, icepacks, a towel that's been put in the freezer (peg it to a coathanger and put a washing up bowl underneath to catch the drips), aim a fan on it and as the air passes by it will cool it down, but this will increase the humidity as the water evaporates into the room. A regular fan used this way will probably do the job a lot better than a cage fan - so yup, bit of a gimic!