Unless your water heater actually plugs into the wall you have no worries. Few residential units are plug in so I will assume that the igniter is simply a piezo igniter which power outtages do not affect at all. If you water heater plugs in then there will be no hot water after the tank cools off but when power is restored the burner will fire and all will be good.
If the pilot light goes out it will not heat the water in the tank. If the pilot light has not gone out it should not affect the water. If you need to relight the pilot light you will have to do it with a match.
If the you are having a power outage, then your gas water heater will not work if it has an electronic pilot lighter. The pilot light does not constantly stay lit so if the power goes out the pilot will not relight to heat the water.