[TomCat]

If you are running a residential fridge off of an inverter it seems highly unlikely your standard TV charge can keep up with the draw. I'm not sure how many amps the charge line from the TV can supply (maybe one of the smart people here knows), but doesn't seem like enough to keep up with the draw from the fridge. In my experience it seems more like a trickle charge that will keep your battery topped off and from depleting while traveling. Depending on your battery bank size, battery type, and how far and how often you travel you may want to look into a DC to DC charger. This would also give you the benefit of smart charging (removing the risk of overcharging). It would require a separate charge line. Maybe not necessary in your case, but something to think about.