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Some quick research indicates that while we won't lose our water per se, there are potentially other issues along that line of thinking: https://www.caltech.edu/about/news/hydrogen-economy-might-im... (2003)

Edit: you might be thinking of helium, which is inert, and so I believe does escape the atmosphere more easily.

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Hydrogen escapes the atmosphere because it is extremely light and the planet's gravity cannot hold on to it.

That just means you've invented a new fancy way to combat rising oceans!

(No, in reality, we have nowhere near the power to make appreciable amounts of hydrogen escape. Even if you electrolyzed water continuously with 2.5 TW of power, which is roughly global average electricity generation, you'd lose something like 4 cubic kilometers of water per year. The Earth meanwhile has over a billion cubic kilometers of water in its oceans, so you'd need over 250 million years to make them disappear.)

Only if the hydrogen is very high up. Hydrogen released at ground level will almost entirely be oxidized before it can get that high.

Yes Helium is the other gas that does this too - but Hydrogen is lighter than Helium.

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