If I call you all fools now, with out testing it myself, I myself would be the fool. I guess my opinion would be, wont work. Well it will work, but your not going to get something for nothing.
If say electrolysis was >%100 efficient (meaning you can get more energy out from the combustion, then it took to separate the O and H) then one could pump the H and O mix made by electrolysis into an engine, in-turn running the engine, then have a generator on the output, feeding more electrolysis (using the byproduct of water to replenish what was converted in the electrolysis process) you would have a continuous running process.
You might be able to time trade it so you dump your Hydrogen load all at once, increasing you fuel eco. for that short bit of time, but your still putting a heavy strain on your alternator, consuming gas.
IMO you'd get better outcome reducing your motor size (and reducing weight), and just pumping the Oxygen directly into the cylinder allowing for more fuel to be added, increasing your power output of a smaller motor (kinda like NOS, just alot more dangerous

)
Good Ol' Wiki:
QUOTE
The energy efficiency of water electrolysis varies widely. The efficiency is a measure of what fraction of electrical energy used is actually contained within the hydrogen. Some of the electrical energy is converted to heat, a useless by-product. Some reports quote efficiencies between 50% and 70%[1] This efficiency is based on the Lower Heating Value of Hydrogen. The Lower Heating Value of Hydrogen is thermal energy released when hydrogen is combusted. This does not represent the total amount of energy within the hydrogen, hence the efficiency is lower than a more strict definition. Other reports quote the theoretical maximum efficiency of electrolysis as being between 80% and 94%.[2]. The theoretical maximum considers the total amount of energy absorbed by both the hydrogen and oxygen. These values refer only to the efficiency of converting electrical energy into hydrogen's chemical energy. The energy lost in generating the electricity is not included. For instance, when considering a power plant that converts the heat of nuclear reactions into hydrogen via electrolysis, the total efficiency is more like 25%–40%.[3]