If you're concerned about storage then your propane dector will kill it too, as will the radio and other parasitic draws. If the trailer is parked and not being used the batteries need to be disconnected, not just the inverter. You cannot plan to leave the batteries connected over the winter.
It's not a whopping amount for a weekend of camping. Sure it's nice to shut if off from the inside, but I fail to see the need to.
IMO, you would have done better to spend the money on a pair of 6V batteries and a battery disconnect switch, or a non-WFCO product... but that's my 0.02 YMMV.
