At least not if you are using an alternator driven by the engine to produce the electricity to generate your hho. First let me say that I got my degree in AMT, and I ran my own auto repair business for many years, so I know what I am talking about. This would violate Newtons first law, it will take more power to drive the generator that makes the electricity to produce the hydrogen than it will give back to the engine, period.
I'm, not saying that this is entirely impossible, hho can be used to improve efficiency IF, and only if, you find another way to get the electricity, from something that is otherwise wasted, like HEAT. Gasoline, after all, is only about 10% efficient. For every 10 btu's created, 1 drives the engine, and 9 go out the radiator. Consider this: https://en.wikipedia.org/wiki/Automo...tric_generator
A thermoelectric generator is the the way to do it, and the only way, imo.

If you really want better fuel economy, use premium gas (always, they sell cheap gas because people seem to be willing to spend more at the pump, to get a lower price!) and add a few NAPTHELENE mothballs. READ THE LABEL, they also sell "para" mothballs, since it's cheaper, but paradichlorobenzine is not mothballs, it's URINAL CAKE, and you don't want to put that stuff in your gas. If you read the labels on the bottles of "fuel stabilizer", or "octane booster" at the parts store, all they are is naptha, at a markup that defeats using it to save on gas. NAPTHELENE is the solid polymer, and it disolves back into naptha in your gas tank. I know there are naysayers to that, too, but this works, I have done it, and usually see a 50% increase in fuel economy over regular pump gas.