In this case he will not be "towing" anything, he will be carrying the motorcycle on a hitch based carrier. The difference is that all the weight (300 lbs + the carrier) will be borne on the RV hitch itself and the RV frame extension (if any) and not just the almost negligible tongue weight of a car hitch while towing 4 wheels down.
Just be sure that the hitch and RV frame attachment can take that kind of vertical or tongue weight. What is stamped on the hitch itself is not necessarily the vertical weight the RV rear end was designed to handle but this information should be available in your RV documentation. Most C class coach hitches will vary from 3000lbs (300 lbs vertical weight) to 5000lbs (500 lbs) for towing. As far as the engine/transmission is concerned, there is not likely any problem.
Adequate for the job??, That will depend specifically on the coach manufacturer and the make and model of the coach, as any frame extension and the hitch were both added by them. Any hitch rated close to a 300 lbs hitch vertical weight will be questionable and you might be better off using a trailer. Some have modified the rear end and use two hitches to carry that 'platform' for the bike.
