The only way the Water heater can use batteries is if you do a very poor job of installing a very large inverter... So the answer is no it won't.
On my coach the fridge will not go to 12 volt power either I can switch it so it gets power via the inverter, but normally that is not done. (Manual transfer switch) (I do this because the bedroom is on the same breaker, I switch the Manual switch to OFF, then lock the Fridge on PROPANE, then switch only the bedroom, and in the old days the ice maker, to INVERTER) that way all my plug in stuff like the cell phone charger work).