I don't see how this would be a problem. Combination PT clinics/gyms are increasingly common. Here's an example of one: http://elitefitcenter.com. My wife is a dietitian and we've actually floated the idea of opening up some kind of wellness center with PT, nutrition counseling, gym, etc, after I finish my commitment with the Army.
In my previous job, I worked as a fitness gym manager. Owned by a PT. We had 4 facilities that were both PT and fitness, and two clinics that were only PT.