Carbon is an element. Most organisms to a lot of chemical rearrangement of the element, but the element is not created or destroyed in biological processes. Any carbon kept during life is released at death.
But not necessarily released as CO2, which is what "re-emitted" means to me. If it goes atmosphere -> tree -> fungus -> bits of fungus buried in the ground for millions of years, that's effective sequestration.
It may well be, but that's not what happens to most of the wood in trees— most of it rots (CO2 released slowly by the organisms consuming the wood) or burns (CO2 released by combustion).
We have found shells, made of Calcium carbonate, still relatively intact more than 3000 years after the death of the animal. Some shells had last for 500000 years (See Nature 2014-dec-03)
Under the sea there are entire ecosystems based in dead shells.