Can a drummer be too busy in a shout? What about a guitar player?
If so - then why can't an organist be too busy?
In my opinion, during the shout, the drummer and the bass player were the foundation. The organ was the lead instrument and there were no other lead instruments or vocals so the show belonged to the organists. Its just an unwritten rule in the book.
Now if he had been doing all of those runs and ideas with lets say, another board player or guitar player, it probably wouldve sounded like a mess because there is no way someone could follow all of that.
But he was by himself which allowed him the space and freedom to stretch.
So to answer your question, yes an organist can be too busy if he's running over other musicians.