The only problem with battery - interter - power is that the heater is going to constantly call for heat - power. Batteries can/will be depleted without shore or generator supplement.
We have an older unit (assumed less efficient than newer stuff) in our home under the kitchen sink adjacent to the den (where I spend far too much time). It kicks on about once an hour for a minute or less. It's very convenient for washing a very small number of items or getting hot cereal or cocoa going in the morning. Beats running the sink water for about a full minute to get hot water from the main tank. And the water is much hotter to boot.
The load of the linked unit (120v @ 6.5a) would translate to an inverter load of, say, 40a at 24v. Not insignificant but the duration is pretty short. It would seem to be a simple matter to provide a switch to turn it off when battery conservation is more of a concern than convenience.
Since the unit is already there and involves little to no startup cost, in my opinion, based on absolutely no experience with anything more complicated than a Class A S&S years ago, it's well worth the effort and the inverter would be a great way to power it.
Real world experience from folks who have been there and done that should be taken with a great deal more weight than what I've said. These are just thoughts from a couch potato who fancies himself as a budding busnut.
Enjoy your dream.