Certainly not in BJJ competitions, hence my confusion at this being brought up. In truth, JJK comps tend to be rare and happen in conjunction with seminars/camps and the like. While I'm not sure I can claim that *my school* is competing, I know of several representatives that have/do when offered. Being that my club trains both Judo and the Jitz, and many people in the club cross-train, I think the board of directors prefer to organize Judo comps and have the ones that want to compete do so there.
If I had to be brutally honest, however, I'll confess that competition is not a priority in the club. The reason for this, I think, is that while we have several really enthusiastic, ambitious blue-belts that really give it their utmost, Ju-Jutsu Kai is very inclusive in its mindset, to where everyone "should be able to participate"; as of late, we've gotten a lot more "casual" practitioners than we have "hardcore/serious bizniz" ones, that really just wanna come in and get a workout/meet friends/ et cetera, and this compels my instructor to customize the teaching/training to his customers, understandably.
So in short, my instructor is pretty slow-and-easy with the people that have, ahem, "performance issues", but is still good at helping the more capable/interested students reach their full potential, though sometimes by suggesting things outside his own Dojo. Somewhat regrettable, but understandable.
But then, I don't know crap, so I shouldn't be thought of as much of an authority on the subject.