That's the argument at least of a recent Nature article. For those who prefer slightly less academic English, here's a bit of a summary from the Telegraph:
Grasslands, savannahs and forests are in a constant battle. Savannah is the area which is being fought over at any one time: can the trees establish themselves in sufficient numbers to create forest or is there something holding them back from doing so? A lack of CO2 in the atmosphere, seems to be the limiting factor. If we increase the amount of CO2 then the trees do better and new forests grow.
Burning more fossil fuels therefore seems likely to grow several new Amazon style forests across Africa and Latin America.
It seems that previous research has really focused on how commercially-important crops perform under increased CO2 concentrations. BTW, here's the author's view of climate change:
I don't think the whole thing is a scam. I do think that the economy with the truth comes at this point, where we're trying to work out how large the effects are going to be. I seriously suspect that positive feedbacks are talked up while negative ones are downplayed leading to the overall effect being exaggerated.
That strikes me as a not-unreasonable view.