This answer is my opinion as a technician to the simple question:
If my water heater is left on, and the water is shut off, will this damage the gas fired water heater if the hot water will not be used very much, or not at all?
Considering you wont be using the water, and it will only be off for a short time there is no risk at all. You can also shut off the cold feed valve to ensure water isnt siphoned out of the tank if cold water is used with the tank off. This would also not allow much hot water to be used out of the tank as you have now air locked the system.
The water heater will still turn on and off to maintain the water temperature inside of the tank. Think about if you have ever gone away for a prolonged period of time. Normally there will be no water use for days or weeks and this causes no problems to the tank. Even if water is used from the tank most (if not all) water heaters have low water cutoffs built into the unitroll (or aquastat). Now The tank has a dip tube for inlet. This dip tube normally stops 4 to 8 inches above the unitroll (which regulates temperature of the water). This ensures that for whatever reason, if the cold supply looses pressure, the water inst siphoned out of the tank completly. This avoids the tank being "tricked" to continuously run to try to maintain temperature if all of the hot water is used up. This also avoids the possibility of a melting dip tube or catastrophic failure of the tank.
Realistically there is no danger to having the tank on with the water off. Especially since the tank works off water pressure to supply hot water. The tank pressure will be equal to your water pressure. If there is no inlet water pressure, there will be no outlet water pressure.
If shutting off your water and leaving your water heater on could cause damage or catastrophic failure, then water heater manufacturers would be up to there necks in law suits. Even if it did cause issues, all the parts, and even the labor should be covered by the manufacturer.