I guess you'd get little H2 out of it while pumping the water all the time, it would be less energy-efficient than electrolysis.
I suspect you'd be right, but thats not for granted.
Who need pump when the rain does that for you.
For the record, I'm wrong. Hydrogen peroxide is H2O2, so it's just adding an extra oxygen from the air to the water molecule. I was thinking about Hydroxyl which is OH and would cause excess hydrogen gas.