I don't think you quite understood tdvance's idea. He's asking what the deal would be if Jupiter's gravity were the only issue. Your retort is that his proposal doesn't solve the issue of Jupiter's gravity. Well...duh! That was the whole point!

The answer tdvance was looking for is that the energy required to lift the hydrogen out of Jupiter's gravity well totally overwhelms the potential kinetic energy which the hydrogen could provide.

In the upper atmosphere, Jupiter's escape velocity is around 60km/s. That requires an input of 3,600 megajoules per kg of hydrogen lifted (assuming perfect efficiency). In contrast, the energy of the hydrogen fuel is only 143 megajoules per kg.