Short answer: Yes, I have seen it and yes, I have done it. In competition, maybe? When I used to watch American Shooter on TNN, they showed some pistol competition. Lots of running around, quick reloads, multiple targets. I don't recall seeing any prone position shooting with pistols, though I might have missed it.
I shoot IDPA but I never went prone during our competitions. We have a guy who sets up the scenarios who has bad knees so we only compete in things that he's physically able to do.
I've gone prone to hit some far away targets.