Yes, but like Larry said, that is not competition...that's people.
When was the last time you saw that kind of mentality in an aikido dojo? I really beat you with that kotegaeshi? Then uke gets up and starts fighting with nage for real? Even Tomiki competition was created with something else in mind besides win-lose.
Actually, I do know of places/events where that has happened. It usually follows this format:
Nage tries to throw uke with kotegaishi nage and fails. Uke says "that won't work on me if you do it like that." Nage get's upset, tries again, but harder and still fails...and maybe tries to punch uke in the mouth. Uke prevents this, but both end up on the floor rolling around. Instructors come over and separate them.
This exact scenario HAS happened. There are people on this board who witnessed it. At an aikido seminar.