Advice: Vacant house during hospitalization?

My brother will be hospitalized for most of the winter. His old, uninsulated house is heated ONLY by space heaters. Low temps in the 20s at night, with occasional single digits. I have had the water turned off at the street and will run a small (safe, oil-filled) space heater, checking it every day or so. If I open the water spigots & empty the pipes, must I also turn off the electric water heater? I was hoping it might provide SOME extra warmth. Thanks.