I like your idea, but perpetual motion is not possible. In theory, we can not create energy, we just change it from one form to another. I suppose if you had an incredibly efficient generator then it could possibly work. Most internal combustion engines are about 35% efficient. What that means is your asking the generator to be able to make enough HHO to power itself and what ever you decide to run in you home with only 35% efficiency. Also I believe the normal HHO generator is about 60% efficient. That means that between the two items your loosing over half of the energy it takes to make them work. It could work if you had a second source of fuel for the generator and only used the HHO as a suppliment. I may be wrong about all of this though.
2006 Ram, 5.9 cummins HO. 4 cell design, 1.5 LPM@30amp, 24.3 MPG