Plumbing – do water heaters shut of when they fail

Unless you have some phantom water supply, the water you are seeing is standing water from pipes higher than the ballcock valve you are trying to change. Is there a hot water mixing valve connected to the cold supply for the toilet? This is common to supply warm water to a toilet to control sweating. If so, is the water heater at a higher level than the toilet valve? If this is the case, try shutting the supply to the mix valve. With all that said, you may have to simply put a collection vessel under the offending tubing and let the water drain out. It will stop eventually after all the standing water above it has drained off. If you open the faucets on other fixtures located higher than the toilet, the draining will happen faster. Of course, an obvious check would be to assure the main shutoff is completely closed, and not leaking by.

If you have no separate shut off valve you should wait till the local water authority can come and temporarily shut off the water at the meter (which is presumably near the street).

I see no problem with shutting off the water supply to the water heater as a short term measure to curb the water waste from the leaking faucet in the shower. It would be a good idea to turn off the water heater during the time that the water supply is turned off.

After you turn the water supply back on the only issue you will have with the water heater is that some air could have fed back into the tank. All you have to do is to open the hot water valves in several of your sinks and let them run for a short while until the water runs clear without any bubbles or spitting coming out of the faucets.