smatthew wrote:you're right - the battery will eventually charge - given enough driving time and assuming there aren't any loads on in the trailer.
The problem is that you never are able to develop high charging currents over the long wires from the vehicle alternator to the trailer battery. As more amperage tries to travel, the voltage loss increases.
Doesn't hurt to do at all though. It's "free" battery charging. I just wouldn't recommend using it as your only battery charging.
Coincidentally, this past weekend, I discussed this very topic with a major Travel Trailer manufacturer factory rep at the annual RV show.
In summary, the longest pickup truck lengths (for example Dodge Ram Crewcab @ around 17.5 feet) have no problems charging a trailer battery(s.) As long as the proper sized wiring is used to the connectors, the trailer battery will charge at a nominal rate. Of course there are many variables to this including state of battery health/age, state of actual discharge before charging, state of TV and trailer electrical system, ambient weather temps etc.
After all, there are hundreds of thousands of trailers out there, of which, a large majority do not have generators, solar or any other methods of charging the trailer battery other then when connected to the TV.