Do these models also tell us how solar radiation at the ground surface will change as humidity and cloudiness might change?

The models do simulate humidity and cloud changes, and hence the effects of these changes on solar radiation at the surface. The question is how good are these predictions. For instance many global models have too much of a seasonal cycle (ie too little clouds in the summer over land). And different models will disagree on the sign of the changes. Global and regional models do not always agree on this.