You need a suitable extractor fan regardless of lamp and environment (indoors).
Lots of people use P.C fans but i would recommend investing in the proper extraction system.
Ludacris, LED's stay so cool you can place your hand on them, and they only feel warm, not hot. They do not produce enough heat, to even facilitate efficent rates of photosynthesis in many cases.
When greenhouse growers starting using them, they found their biggest problem was a lack of warmth. Even though LED were saving them big time on electrical use, compared to HID's, this was soon found not to be a positive, since many of them had to add a source of heat (which the HID's had provided on their own in the past).
Turning the closet into a wind tunnel, will just add to this problem. A simple inlet fan, with a passive exhuast up top, will fill the bill quite easily, no need to spend money that works against you. If he were running a HID, then I'd be the first to agree with you.