I’m guessing a tankless water heater involves some electronic controls. It probably could be designed to use low-voltage DC with a battery backup, but that would be fancy.

It definitely has to if it doesn’t have a pilot light, else its electrical ignition won’t work, but if it has that, there are various ways you could make it work, including just using the heat from the pilot light to drive a thermoelectric generator to get a small amount of juice.