no. Unless the tree vaporizes or burns, none of it gets back into the air. It is for all intents and purposes a permanent lock up. Mankind is the gatekeeper of whether to unlock this carbon prison in our choice to burn oil or wood.

Trees aren't the complete solution and the reason why has nothing to do with the tree dying and releasing the carbon.

What's going on here is that plants are converting CO2 into mass. A tree that isn't growing isn't creating new mass and therefore isn't lowering carbon in the atmosphere.