What typically happens to H2 molecules released into atmosphere (with no spark source)?
The most common, reactive stuff in the atmosphere are $\ce{-OH}$ radicals (Wikipedia). So I guess they're the natural antagonist for $\ce{H2}$ molecules.
Btw., as soon as it's diluted in the surrounding air, it will no longer rise. Only bulk masses have buoyancy. The g gradient in the atmosphere is much too small to separate gases.
In the end, hydrogen however does diffuse upwards and is ultimately lost into space. Hydrogen and helium are light enough to be able to reach escape velocity in the upper atmosphere.