Neither gas nor electric tankless water heaters provide hot water if the power goes out. While a gas-powered storage tank unit can't warm additional water during an outage (since they use electricity to ignite the pilot, maintain temperatures, and detect hot water supply need), the existing full tank of warm water might be enough for your needs. However, since tankless units don't have a reserve, you'll have no hot water whatsoever from your tankless unit during a power outage.