And neither is your conclusion in this matter.
A simple way to prove the whole design would be to have a bottle of the gas installed that could be switched on by design.
Then run without it on, and with it on, and compare the results.
If there is no positive results from running with the bottle turned on, then no amount of gas generated by using the alt could do any good at all.
But as was pointed out upthread, there have been tests of internal combustion engines that have shown a positive change in energy output, a cleaner burn, and a cooler running system using small amounts of HHO gas to supplement the normal fuel.
Whether those gains are large enough to put a bit of extra load on the alt is the real question.