Sure, but before then it's stored. And if trees are constantly creating new biomass, you've perpetually buffered an amount of carbon equal to (annual production x time variable). The first variable is limited by the thermodynamics of sunlight, so do what you can to approach that limit. Then the main target of innovation becomes, what forest management techniques can maximize that time variable?

By default about half of a tree's absorbed carbon is injected into the ground to build soil, as root mass and root exudates. Plus trees drop mulch -- mainly leaves. Soil carbon is only released when the soil is destroyed or eroded away. So... don't do that. :)