Let's see. Running microwave when gen is on to charge batteries actually uses more fuel since the load on the gen goes up with the use of the mwave. Maybe not noticeable but there is no such thing as a free lunch.
When we were dry camping in our former coach with propane/electric water heater we turned it on 15 minutes before we expected to use it. For normal warm water to wash hands etc the tank usually would be fine even though it had been off of a few hours, it is very well insulated, thus you are not heating from cold each time.
We were less interested in the cost of propane than in preserving it so we didn't have to break camp and drive to town to refill. In the scheme of total cost of operations propane is small potatoes.