Can I damage my water heater by turning the gas valve to the off position?
No it wont hurt the water heater. Turning the gas on and allowing the burner to operate with an empty water heater would damage it, but no gas, with or without water in the tank will not hurt anything. 
Be aware, water left in the tank may smell like rotten eggs until flushed for 10 mins or so prior to use.
It would be ideal to shut off water supply to water heater, shut off the gas on the control valve itself, and drain the water heater.
When youre ready to start using it again, simply open the hot side of a faucet, turn on water supply to the water heater; faucet will spit and blow as the air purges from the hot water pipes. Once faucet is flowing normally, shut off hot faucet, set w/h control to pilot, and light pilot flame per w/h instructions, then follow w/h instructions for setting water temp.

Just NEVER operate a water heater,  gas or electric, with no water in the tank.