You've got to take it on a species-by-species basis. Take, for example, Sequoia Sempervirens. Right up until the trees fall down because they outgrow their root systems, older trees put on more mass and thus fix more CO2 than the same area filled to capacity with younger trees.
Then they die, and decompose, releasing nearly all that CO2 back into the atmosphere.
Even trees which aren't getting taller are often getting thicker, so the question for a given species is whether younger or older members put on more mass for a given area. Virtually all of the non-water mass of all vegetation is carbon, and nearly all of the carbon of all vegetation (even relatively high soil carbon users like corn) comes from the air.
Yes, trees that are growing do take carbon out of the atmosphere. After they die, it gets released back. Hence mature forests are essentially carbon neutral.
Now, if we did something else with the dead wood, such as burning it instead of coal, or using it as a building material, it would be a net positive (perhaps not ultimately with the latter - nearly all wood rots eventually). Many species and ecosystems, however, are dependent upon rotting trees; removing them could have adverse effects on the ecosystem.