I think Obito is pretty close to genjutsu proof, not 100% though. I dought he can send only his brain away to block out the genjutsu. Just logically speaking if he were to send his brain away he might die. I think he need a "case" or a kind of package for organs or they won't come back improperly, that just makes sense to me though, seeing as the kamui dimension is a void. If he sent it back wrong he could get killed. IDK, but honestly I think he is almost 100% genjutsu proof. Funny how Obito is almost 100% resistant to everything with the Kamui, but Kakashi can't use it nearly as well.