You could if you have access to them to make yourself feel better. We have a stove with 3 pilot lights (it is a seriously awesome stove - don't judge!) and turn off one of the pilot lights because we never use that feature. Have had no issues although I do occasionally stick my nose there to make sure I don't smell gas.
And now you've just reminded me to turn off the pilot light on our furnace. Thanks!
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It all depends on where the leak/plumbing work is. The concern is whether there is any reasonable possibility of something going wrong during the repair that will result in the water heater draining. An empty water heater should be totally off - not even a pilot light.
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If your water heater is in the basement and you are cutting off the hot water coming out of the water heater as well as cold water at various places in order to work on a repair in a pipe somewhere above the water heater then there is very little chance of water draining out of the water heater. It won't come out through the regular hot output because you cut it off. And it won't come out "backwards" through the cold because if the water won't flow upward - no pressure. If there is still pressure because of the incoming water (e.g., if your main house shutoff doesn't work 100%...been there) then new water coming out of the leak will basically be cold water coming in from the outside - there might be some mixing but the water won't magically be sucked out of the water heater.
On the other hand, if the pipe is in the basement, or if the water heater is in the attic, then depending on the exact configuration of your plumbing system, there is a reasonable possibility that some (or all) of the water in the tank may drain out of it when you are working. If that's the case, turn off the gas to the water heater and when you are all done make sure the tank has refilled and then turn on the gas and light the pilot.
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