Interesting topic, and theoretically plausable.
Plant growth requires three basic elements.
Fertile growing medium (soil)
Water (rain or irrigation)
Photosynthesis (sunlight)
Typically, deserts have only one constituent of fertile soil, sand. What's missing, is moisture retaining humous and silt (clay). In a natural way, humous content can be increased by grazing ruminants. But, the large herds of herbivores that will provide the soil enriching dung will need copious amounts of water to drink...where is this water going to come from during the initial phase of desert reclamation?
It is of course true that many of the worlds deserts have enormous underground lakes hundreds of feet below their surface. If such aquifers were discovered beneath the deserts this gentleman wishes to reclaim, then it is far more likely to be used for short-term human food production rather than desert reclamation. A typical example being the Egyptian intrepreneur who, discovering a huge underground lake of fresh water beneath the desert, proceeded to start human food production. The crops, consisting of salad vegetables and fruit are exported all over the world...and making a huge amount of money for him. What needs to be remembered, is such crops consist of 60% water, and he is exporting this valuable resource to countries that have plenty of fresh water on tap. He has stated categorically, when that sub-desert aquifer runs dry, he will simply walk away from the farm....and it will still be a desert.
I admire this gentlemans resolve, but I don't think he has fully addressed the initial requirement of enough water to sustain large herds of cattle or goats during the early phases of desert reclamation.