First, any tow vehicle with a factory tow package is going to have an upgraded alternator to handle the increased load experienced when the TT is plugged into the truck's connector. If you feel the need to connect your camper to the truck because the batteries are low, simply plug it in near the hitch, and it will charge them just fine.
Second, The way a vehicle's charging system works is, the vehicle actually runs off the battery for all it's electrical requirements, and while old fashioned generators had to run at higher rpm's before the charging started, today's alternators produce electricity at very low rpm's, so no need for high idle to charge the battery.
Purpose built generators provide nearly all their generated electricity for such things as battery recharging, which makes them much more efficient than your TV for recharging. Even at that, it takes several hours to recharge batteries to 100% with one.
hope this helps.
