Trees and other plant life store carbon as they grow, and release it as they decay after death.
Forests will store carbon as and while they are growing, but as and when they reach a stable size they will stop storing additional carbon. That is, carbon stored by growth will equal that released by decay.
It will be reduced significantly, but I wouldn't expect it to actually break even for hundreds of years atleast, if then. Some material is always going to keep getting buried deeper and deeper except for a few areas prone to very high levels of erosion.