problem, yes, total impediment, no. For your first tri, you will be fine, but as you get better, you will realize more and more that they just don't work too well.

I can see three real problems, and an infinite number of elitist roadie/triguy reasons. (you may know those already like "Because it's a fixie.")

Problem 1: Hills. If a hill gets too steep for your gear ratio, you won't be able to keep your cadence at the right speed. Then if you go back down the same hill, you will not be able to go nearly as fast as anyone who can freewheel. Your knees might also explode.

Problem 2: Turns, when you can freewheel, you are supposed to keep your outside leg down to be more stable and if you are leaning and you are close to the curb, your inside foot won't hit the curb or the ground, causing you to crash.

Problem 3: As you progress and get faster, you will need a range of gearing to keep your cadence just where you need it.

For you first tri, it will be fine, but after that you will need to think about something with gears and probably aerobars.