Reversing the desertification
It would depend on the reflectivity of the material used - a lighter color will reflect more solar radiation and help cool an area fairly quickly , but it would take longer for the area covered with such structures to experience changes in  poleward. energy transport. The poleward heat transport determines where the jet streams are located and how far north and south tropical rains (intertropical convergence zone) move. Thus, whilst the structures would cool the area, there would likely be insufficient rainfall to re-establish substantial plant life and reverse desertification. 

In short, because of the need for water and the mesoscale weather patterns in a desert, shading the deserts would have little effect on the rate of desertification.