I would worry that your Hydrogen atmosphere would wither away. Simplifying a bit, there are two mechanisms at play.
The molecules making up the atmosphere have their velocities distributed according to the so-called Mawell-Boltzmann distribution. The lighter the mass of the molecules, the broader is this distribution. By that I mean that the lighter the mass, the more molecule will be found in the tail of velocities higher than the escape velocity. The width of the distribution if proportional to the square root of the mass of the molecule, which brings a factor 4 between Hydrogen and our atmosphere.
If the gas in the upper atmosphere is a good absorber of ultra-violet light, then it will be heated up and then this will build up pressure which will push the outmost layers out. Rinse and repeat. If I remember correctly, this effect is actually the dominant one. Unfortunately, I don't have time to double-check, sorry about that.
Just to be clear about the difference with the previous mechanism. Jean's escape considers an atmosphere in thermodynamical equilibrium, i.e. the temperature at any given altitude is constant, and this is a pure effect of the thermal agitation of the molecules. Hydrodynamic escape on the contrary is a dynamic phenomenon.
This is a Jupiter-like planet which is estimated to loose from 100 to 500 million kg of Hydrogen per seconds! The Wikipedia article has more details.