Here's the problem: if we did this and it managed to stop global warming in a significant way, then we'd
still be producing carbon emissions.
And if you believe that carbon dioxide, methane and other gases act to trap heat within the Earth's atmosphere, then at some point you have to stop pumping billions of tons into the atmosphere if you want to stop global warming.
So perhaps the un-desertification would help curb global warming, but if we continue to spew greenhouse gases into the atmosphere, then we're just delaying the problem.
I don't think a carbon tax is a good idea. I think other things will reduce our emissions:
1) Investing in technologies to produce energy from sources other than coal or gas such as hydropower, nuclear power, wind or solar. Rather than spend trillions of dollars irrigating and up-keeping a forest in the Sahara for untold centuries, it would make more sense to cover about 2-3% of the Sahara in solar panels. It may cost trillions of dollars to do such a thing, but not only would it require far less upkeep and irrigation, it would also help power the rest of the world and would essentially make coal and gas power plants irrelevant. If we cover ~1% of the Sahara in solar panels, it would be enough to power the whole world at 2005 levels.
Link.
2) Investing in emission-less modes of transportation such as electric cars and trains while also investing heavily in making denser settlements with shorter commutes and viable public transport systems. Vehicle emissions are a huge source in North America and much of that is because of long commutes in cities suffering from urban sprawl.