If you increase the heat during combustion due to adding hydrogen, you will increase the NOx output.
But does this tiny amount of hydrogen increase the heat given off by the internal explosion?
It seems to me the only way this adding of the Hydrogen and Oxygen from the electrolysis of the water could create an end benefit to the cars MPG would be if the engine actually ran cooler, converting more energy into HP and less into heat. Because that’s the only two directions the energy is going to go... mechanical energy and heat. The small (and it must be incredibly small amounts) of hydrogen being added adds that much in terms of BTU to the combustion chamber.. but the O which is the other product of splitting the water molecule may be causing the fuel to burn more efficiently, and thus more energy gets transfered to mechanical than heat? I dunno.. but I woudl think you’d have to run cooler in the mixtures they are probably winding up with, to see any discernable MPG increase.