so, while he's at it.... is he also gonna invent the "perpetuum Mobile" to power his bike?
Besides the fact that this is stupid, because:
1) he's gonna get shot before he can even get off the bike and explain himself at a military base. (can you say "IED"!)
2) the very very small ammounts of hydrogen wont even be notiveable to the large ammounts of air his engine draws....
.... keep in mind: Liter engine at 5000 rpm draws: 1 * 5000 / 2 = 2500 liter per minute ~ 5200 galon of Air per Minute. how many galons / minute does his contraption produce? maybe 0.01 gal / minute?
now for the real reason why thsi wont work:
1) The separation of Water into 2 Hydrogen molecules and 1 Oxygen molecule consumes Energy.
2) The "burning" of Hydrogen and Oxygen releases Energy.
the energy created in step 2 is always (equal or) less than the energy consumed in step 1.
In the case of "equal", you would assume a 100% efficiency, which is in the real world never possible.
if the energy in step 2 would be LARGER than the energy consumed in step 1, you would be CREATING energy, which is not possible in "traditional" physics.
Now, for practical terms:
How does he generate the electricity for powering the electrolysis?
Likely from the "generator", or "Stator", which is engine driven.
The engine needs to work harder to generate this "extra" electricity. Similar to e.g. your gas mileage going down when you turn on the AC.
since your engine has a ~60% efficiency, and the generator another ~80%, lets say: For every ammount of hydrogen energy created (measured in Joules), you need to burn twice as much energy in gasoline.
If you now burn this energy again and free up this energy - then you've still effectively wasted gasoline.
so - from a physics point of view.... an all around stupid idea.