I've competed in Tri's with a Fix numerous times. Triathlon rules mandate a bike ~must~ have front and rear brakes. This is sometimes parenteticated with "no fixed gears". Although the intent is obviously to keep someone from arguing leg-braking does not constitute a rear brake, it could be mis-construed by an official. For this reason, I always have a freewheel on the flop, in case.
Having said that, there's a new trend for draft-legal tri's. These rules tend to mimic UCF rules, DD frames, No aerobars (beyond the drops), etc. I'd imagine they don't allow FGs, but really dont know; I refuse to race in a draft-legal tri (tarnishes the sport, IMO).