Are you serious? They do it all the time- to take hand offs from team cars, to don/doff clothing, to stretch, whatever. It takes a certain amount of balance and core strength, but it's really a fundamental biking skill, IMO.

I used to be able to do it all the time on my old bike, and could quite easily take off/put on vest/jacket, arm warmers, eat, drink ,stretch, or just relax. Not a problem with small bumps, especially if you stay relaxed, and it's not all that hard to make fairly decent turns. My current bike is too twitchy (especially in any wind) and I'm sad about that, cuz otherwise it seems to handle quite well.