Water heater problem?

I have two water heaters. The main water heater is solar powered and the backup is on propane. When there is company I need the backup but when it's myself I just need the main, so I disconnect the propane. Should I also close the valve that runs hot water from the main to backup (this hot water pipe feeds the propane heater and the house)? Or does the propane heater act as a storage device for hot water?