No, you are carbon neutral. The most obvious (though maybe not best) way to do this is turn separate water into H and O, then store the H in a tank. When you need more power you burn the H getting water back. This process is not very efficient, but when power is cheap who cares.

You can also turn CO2 into synthetic oil (Methane, gasoline, Jet fuel, motor oil - your choice of what you want) via known processes. Again the process isn't very efficient, but when the inputs are free who cares. The sum of is carbon neutral.