It's not as simple as all that. Adding more oxygen than the stoichiometric ratio requires won't help. However, it is possible that the device in the OP delivers all the electrolyzed gases to the engine, in which case it's fortifying the normal fuel-air charge with the exact ratio of hydrogen and oxygen to get perfect combusion... no hydrogen or oxygen left over. I would think that this mixture would be extremely ignitable, more so than the regular gasoline-air mix the engine usually gets.
But doesn’t the hydrogen-oxygen mixture burn at a much lower specific heat than does gasoline and air, much less gasoline and oxygen?
The only benefit I see (if that is correct) is that the spark plugs will last longer ;-)