I have ridden without brakes on a fixed gear bike, I found it mostly fine as even with brakes I don't touch them, I've a set of black anodised rims 2 years old and the braking surface is barely marked (it only takes one wet ride to take the braking surface anodizing off if you use your brakes) but I acknowledge it was IMO a silly thing for me to do despite being confident doing it at the time (I added brakes as an in case measure, and also for comfort as I like drop bars and brake hoods, and aesthetics, so it looks like a proper road bike). If you have to ask the question, you obviously are not confident in doing it, so don't bother! Not to mention the legal implications!