Can the water heater be damaged if the gas has been shut off?
That depends. If the water heater in question has a pilot light, as opposed to an igniter, then probably not, but if there is an igniter and not a pilot light, the fuse for the igniter could blow as the igniter tries to light a nonexistent gas flow. As far as physical damage to the water heater itself, I don't see how. A fuse is a pretty minor fix. And if you turn the thermostat all the way down, you shouldn't have to worry about the fuse either.