I'm not sure I understand your setup, so let me assume it is like mine. At the bottom of the water heater is a drain valve with a hose fitting; you need a silcock wrench to open it, and when you do, water will drain out by gravity, even if the main water supply from the County is turned off.

The hot water supply comes out of the top of the heater to supply the house. Pressure from the incoming cold water propels the hot water around the house and upstairs.

So, if the main water supply to the house is out (County water is off), I can access water from the heater from the drain valve at the bottom because it is gravity fed. But no water is available elsewhere because there is no pressure to propel it out of the top of the heater.

If your setup is like mine, the water from the heater that you want to access at the washing machine may not flow by gravity; the water may need the incoming water pressure to reach the washing machine. As with many such situations, the devil is in the details of the setup.