No, I let it fill with air at the top. That's why it says "air" :P It sinks because air is heavier than HHO and the container is carefully balanced to be bouyant with HHO and sinking with air.
I think it's the same as your idea. I just drew the HHO generator outside, but it could have been electrodes in the container itself. Neither is ever subjected to the water pressure at the bottom of the main vessel.
There's no pumping of water or gas. The air just drifts out at the bottom as it's displaced by HHO, and drifts in at the top as the HHO is used by the generator. You could have a membrane to keep the two gasses seperated.
You could also generate excess HHO at the bottom and burn off what doesn't fit in the container, driving the generator. But you may as well burn it at the top because there's HHO in the container when it gets to the top. Also, the less burning you do, the more siginficant any bouyancy power becomes by comparison.
