Every one of these that I've dealt with monitors the fan, if you disconnect it the PSU will shut down.
Some power supplies of this type are very quiet though, I have some IBM 39Y7201 that I got on ebay, two for $16 shipped, that's practically free. I use them to power my RC LiPo chargers, one single unit and another pair I modified for series operation. I really like these particular PSUs because they're compact and nearly silent. The fan has an internal thermal control and ramps up only as needed.