This is a good question that is being actively investigated.
I think the idea is that the C stored in the permafrost has been accumulating for thousands of years, and yet could release in just 10s of years. So even if there is increased vegetation growth (which is predicted), there is unlikely to be enough rapid growth to offset the release of thousands of years of accumulated C.
Full disclosure: I actually work for a modeling group with the University of Alaska Fairbanks/Institute of Arctic Biology that is investigating these sorts of questions.
I think the idea is that the C stored in the permafrost has been accumulating for thousands of years, and yet could release in just 10s of years. So even if there is increased vegetation growth (which is predicted), there is unlikely to be enough rapid growth to offset the release of thousands of years of accumulated C.
Full disclosure: I actually work for a modeling group with the University of Alaska Fairbanks/Institute of Arctic Biology that is investigating these sorts of questions.