Even with electric we put the water heater on first thing in the morning, then turn it when we go out, or even if we are in the van. Tends to go back on later afternoon and stays on until supper pots are washed up. So even on gas it wouldn’t use much at all.Heating the water using lpg when you're on ehu obviously wouldn't make sense, but it's not prohibitively expensive as an alternative when no other power source is available.
We've often rallied off grid with the fridge and the water heater on lpg.
We didn't leave the water heater on for long periods of time, and sometimes it's easier and cheaper to put the old whistling kettle on for washing up off grid.