I have an Atwood 6 gallon propane only pilot model.
When not using water, the main burner seldom kicks on, and when it does it is only for a few minutes.
Seems like you would not really save any propane turning it off for the day, as the burner would have to run a while after being off all day to reheat the tank.
IE, leave on all day, burner kicks on 3 times through out the day for 5 minutes each time, OR, turn off WH in morning, fire back up in the evening, and the burner runs 15 or 20 minutes to reheat the tank.