What do you think rain is? Condensed water vapor. Some parts of the world would benefit from more rain. Oceans cover most of the globe and their evaporation in sunlight contributes more vapor to the atmosphere than man ever could. The atmosphere can absorb only so much moisture. When the air reaches saturation point, then the rest will condense and fall as rain.
You're absolutely right, via natural causes. Now you intend to super saturate it via artificial means - burning hydrogen. Rain you say? Quite likely and a hell of a lot of it...........
Nothing like increased water vapor in the atmosphere to increase the greenhouse effect......