To respond to the original question:
Having been involved in cheer for 4 years now, I don't think I would send CP to a gym where the owner had no cheer experience (unless they handled the business end and had a co-owner who handled the cheer end). However, many people join a gym not knowing the background of the owners. The owner may say one thing ("we went to Worlds five years in a row!!!") but not be able to bear it out in how they run the gym.
In my opinion, an owner having credible experience in both cheer and business would be ideal.