Not using the engine to make the electricity is the reason behind plugging it into the wall. The energy that the alternator will consume from the engine will not be made up by the hydrogen produced. This will result in a net loss of energy the source of that energy being gasoline.All this talk about charging batteries to run the HHO/H2 seem a bit academic to me, as most HHO/H2 systems generate the gas 'on the fly'
using the alternator/battery on the vehicle. They don't store the hydrogen in a tank, they just produce enough to replace some - or most - of the petrol that the engine would normally burn.
Using hydrogen as a fuel may be fuel mileage friendly but it is not engergy conserving. It uses more energy than buring gasoline.