Should you turn off tankless water heater when on vacation?
Thereof, should you turn off gas water heater when on vacation?
It's not recommended to completely turn off a water heater, but you can a significant amount of energy—and money—while on vacation by switching the water heater to vacation mode. If you'll be gone during the winter, flush all the toilets in your home to drain the water out of the tanks.
Also to know is, is it OK to turn off tankless water heater?
Yes, you should, if it is for any significant length of time or there will be significant loss of water from the piping. For temporarily allowing repairs it probably is irrelevant, but if for vacation, remodeling, or the like you should shut off the source of heat, whether gas or electric.
Especially since the tank works off water pressure to supply hot water. The tank pressure will be equal to your water pressure. If shutting off your water and leaving your water heater on could cause damage or catastrophic failure, then water heater manufacturers would be up to there necks in law suits.