Around 80% of the reflectivity of the Earth is due to clouds or about 77 Wm-2 depending on which energy budget you like. If you assume albedo (reflectivity) is magically fixed and completely separated from the "Greenhouse Effect" by some strange magic, you are missing a huge portion of the picture. The atmosphere also absorbs in the ballpark of 77 Wm-2 of sunlight mainly due to clouds and water vapor. Clouds, water vapor, convection, precipitation and albedo are all interconnected because of water in its three states.
Warmer air can hold more water and warmer more moist air condenses at a higher temperature. Since temperature decreases with altitude, that would mean clouds would start forming at a lower altitude unless lapse changed to offset the change in dew point. That is unlikely because the mechanical forcing of convection, buoyancy, becomes stronger with increased water vapor. As buoyancy increases the rate of falling colder dry air that replaces the warmer moist air. That colder dry air, which should be colder and dryer thanks to increased GHE would stimulate more condensation, stimulating more convection and more precipitation.
The keys to all this activity are the convective triggering mechanisms, temperature, moisture and pressure differential. One of the odd things about this combination is the role of saturation vapor pressure of water. Colder dry air would have a higher pressure inducing flow toward warmer moist air but the warmer moist air has a higher saturation vapor pressure meaning water vapor would tend to flow from lighter more buoyant air to less buoyant air. This is wonderfully counter intuitive to most folks :) It is also just one of the mechanisms that makes modeling clouds and water vapor a serious bitch.
I am still trying to digest this paper but it looks like it is on the right path.