Let me caveat this message with the fact that I am not any kind of engineering expert. I just read a little... plus I stayed at a Holiday Inn Express once.
I would assume that most catamarans plane since if they were displacement, they would be tied down by their theoretical hull speed. According to the Annapolis Book of Seamanship, hull speed is calculated as:
Hull speed = 1.34X (square root of waterline length in feet)
That would put the hull speed of a 20 foot beachcat at right around 6 knots. So anytime you are sailing over 6 knots, you are probably planing to some degree. Right?