Electronic control of the "tickler" input heat doesn't depend on the original source of the electricity that's generating the heat.
Thermocouples, RTDs, and the control circuits they drive don't care if the original electrical power is coming from the grid, a battery bank, or even an array of solar panels. (If the input power must be AC, an inverter can convert the battery or solar panel DC output to AC. If the input power must be DC, electricity from the grid needs to be rectified to DC anyway.)
Of course that's all true, but remember that one of Rossi's target markets is industrial heating, so he is looking for an E-Cat that "can" be controlled based only on working fluid flow rate, which he has apparently succeded in doing.
And I think he'd like to come up with more and larger E-Cats that exhibit similar characteristics.