These guys have modelled it and it works!
Each year, irrigated Saharan- and Australian-desert forests could sequester amounts of atmospheric CO2 at least equal to that from burning fossil fuels. Without any rain, to capture CO2 produced from gasoline requires adding about $1 to the per-gallon pump-price to cover irrigation costs, using reverse osmosis (RO), desalinated, sea water. Such mature technology is economically competitive with the currently favored, untested, power-plant Carbon Capture (and deep underground, or under-ocean) Sequestration (CCS). Afforestation sequesters CO2, mostly as easily stored wood, both from distributed sources (automotive, aviation, etc., that CCS cannot address) and from power plants. Climatological feasibility and sustainability of such irrigated forests, and their potential global impacts are explored using a general circulation model (GCM). Biogeophysical feedback is shown to stimulate considerable rainfall over these forests, reducing desalination and irrigation costs; economic value of marketed, renewable, forest biomass, further reduces costs; and separately, energy conservation also reduces the size of the required forests and therefore their total capital and operating costs. The few negative climate impacts outside of the forests are discussed, with caveats. If confirmed with other GCMs, such irrigated, subtropical afforestation probably provides the best, near-term route to complete control of green-house-gas-induced, global warming.