Yes, it will work. And quite well. I would (if you are worried about keeping the trailers batteries up in transit) look at
Trailer chargers. They are designed to charge the liftgate batteries on trailers off the trucks power. By eliminating all voltage drop in the charge line from the truck to the batteries, you can fully charge or maintain the trailers batteries under loads (of less then the charger is rated for). The charge line in my truck to my trailer rarely gets over 13.5 volts, even with the alternator pushing 14.4 volts. My inverter/charger keeps my mini fridge running 24/7 except when in storage.
