The advantage is that it is clean. (you are pushing the pollution issue to the power generating plants, where they can use stack scrubbers, precipitators, and other pollution control equipment to reduce pollution to MUCH lower levels that can be achieved with small engines, or auto engines, for that matter.)
However, any on-board charging device, except for solar, will be pollution generating. And inefficient.
And, I hate to burst your bubble, but, the amount of energy you put in to the system is the
maximum amount of energy you can get out, minus system inefficiencies. The energy you put into splitting water into hydrogen and oxygen is the same amount of energy released by the recombination of hydrogen and oxygen. Again, subtracting the inefficiencies. An internal combustion engine is less efficient than a decent electric motor at converting energy (electrical or chemical) into kinetic energy. This means that the system, as a whole is less efficient than an electric motor setup - i.e. - you would go further using the battery to power an electric motor setup than you would in splitting water into hydrogen and oxygen, and then recombining the hydrogen and oxygen in an internal combustion engine.
You say your generator is producing apx. 2.5 liters of gas per minute. This equals 0.11 mole of gas per minute. (2.5l/22.4l per mole @ stp.) This is equivalent to 5.7 kcal of work. (.11 * 52.1 kcal/Mole.) In KWH, this is equal to 5.7 Kcal * 1000 Cal /Kcal * 0.00000116 KWH/Cal = .0066 kwh (Note - IF you are producing 2.5L at 4 psi, then this number should be increased apx. 27.6%, as the gas is more compressed, and you have more mass per unit volume)
However, you put 0.171 KWH of electrical work into the system. (12V * 8A * 1.78 hours * 1 KWH/1000 WH)
This means that your system of producing hydrogen is operating at about 3.9 percent efficiency, not counting the motor, which at best is operating at about 50% effeciency. (Again, if gas produced at 4 psi, this value would be slightly less than 5%)
IF you get a source of "free" energy, i.e. large solar panel or wind electric generation facilities, splitting water into hydrogen and oxygen, and then storing the hydrogen in tanks, will hydrogen as a fuel take off. However, the development of truly high density batteries, produced at commercial quantities, coupled with the inherently low efficiency levels in producing hydrogen gas, may lead to hydrogen, as a motor vehicle fuel, being bypassed entirely.
(Note - the conversion factors and chemical constants come from the 63rd edition of the handbook of chemistry and physics, with the exception of the molar volume of any gas at STP. Ref
http://www.newton.dep.anl.gov/askasci/chem99/chem99360.htm)