I’m no scientician, but if you “green” the deserts, while they would act as a heat sink, wouldn’t the excess water vapor lead to a greenhouse effect that would more than offset whatever carbon was absorbed by the flora?
Now you’re just making sense. ;’)
Of course, carbon dioxide is only a few hundred PPM, and has nothing whatsoever to do with climate change; climate change is 100 percent natural 100 percent of the time; and having more water vapor coming off the Sahara would lead to more rain as well, transforming places like, oh, Arabia, back into verdant places as they were in early historical times, but particularly prior to Islam.