Is a formal physical therapy program necessary after total shoulder arthroplasty for osteoarthritis?

Yes. Physical therapy is necessary to restore range of motion, strength and function to your shoulder. It is also important in minimizing the risk of developing a frozen shoulder post-operatively.
Surgeon Preference. This is entirely dependent on the surgeon who does your surgery. Part of the surgeon's job is to direct your physical therapy after the surgery - some prefer a home program while others send patients to a formal program with a therapist. The surgery and therapy work together to give you the final result, so no matter where or how you do the therapy it is just as important as the surgery itself.