I sometimes go to Yasuhiko Oyama's tournament as a spectator, and see people from other systems competing in the "Knock Down Tournament" there.
There have been people from Yoshukai dojos, even a giant of a fellow from the local Kung Fu school. They've all been well-received, as long as they act with dignity and honor, regardless of whether they win or lose. The only fellow I've known who wasn't well-received was a Yoshukai guy who loudly, and verbally protested the referee's call (and that referee happened to be Oyama Shihan himself).
There were a lot of people frowning at that guy when he starts screaming at Oyama Shihan...
The battles are stand-up fights, and are full contact. Mostly punching to the body, although you'll see a good bit of kicking to the thighs, body, and head.
No punching to the face, no kicking below the knee. If you get knocked down twice (without being KO'ed), then the other guy wins.
Before the competitors can enter the sparring tournament, they must qualify by breaking at least three wooden boards with a hand technique. Anyone who is well-conditioned for the fight should be able to do this.