It theoretically works by breaking down water molecules by a process called electrolysis. The water passes through a series of energized plates or electrodes (cathode and anode) that electrically separate the water molecule, 1 part hydroxide 1 part oxygen. The required amount of energy to make this happen cannot be generated from a 12 volt system. The power can be amplified, but still will fall short of optimal molecular separation. The electricity needed to obtain a state of electrolysis also generates a large amount of heat energy. It would need it's own cooling device to keep itself from burning up.
Most likely, you would end up injecting mostly water into the intake. If you tune lean and mist with straight water, you would see a difference in fuel economy and not suffer the effects of detonation from a lean condition in the combustion chamber. Makes you wonder just how much gas you could save doing this. You can make a water misting system for a few hundred bucks or less.

*EDIT: and Yes, if it worked at all it would work on any internal combustion engine, including the good ole Wankel. N2O works on the rotary, why wouldn't hydrogen? The real question is, how do you consistently generate enough hydrogen to make it worth your time?