I have used a Brake Buddy for many years and towed coast to coast for several days without my Jeep battery going dead.
ALSO it is recommended before hooking up the brake system to pump the brake pedal a few times to clear out the vacuum in the brake booster. Running the engine will keep the power vacuum active making the brake too sensitive.
If there was a problem to be expected it would be addressed in the brake operator manual. I would not run the engine while towing as too many problems are possible to happen as noted by other posters.