Yessir, I have. I raced an indoor mile in college when I had a cold and sore throat. For me, it was a bad idea. After the race my illness immediately became much worse and I ended up with a pretty bad sinus infection. The air in that building was also terrible. The intense respiratory activity inflamed my sinuses and throat, and it SUCKED.
That said, you should also know that this was my first mile race. I had been a 400m guy and was moving up to middle distance, so I was inexperienced. I tried to go out with the leaders, blew up half way, and then just gave everything I had not to finish last. It was a bad race regardless of the sickness. The race was also at altitude, which may have been another factor in my disasterous performance.
So, if you're in shape you might be fine. I was not in shape for the race I was in. If you feel like you are fighting harder than usual to keep the pace, I would consider backing off. You could make yourself sicker.