Can you run the toad engine to recharge the battery-- sure.
Should you run it all the time or while towing? I wouldn't. Big waste of gasoline and needless wear and tear on the engine.
Unless you are in stop and go traffic where you are using the toad brake a lot, running it for 15 minutes at lunch and then charging at the end of the day by running the engine or MUCH more efficiently by using a battery charger on extension cord should work just fine.
OR run a large-gauge charge wire from coach battery to toad battery with fuses at each end.