If that timber stays a wooden structure for several centuries, it would, for that time!
Maybe we should start to build more long-term things from timber, likely we would fire-proof them well. But steel, concrete, and plastics are still much easier to use for long-term structures like large buildings, bridges, roads, etc.
If it's used to produce paper, or wooden packaging, or for making chopsticks, etc, it would likely not. All these things are expendable, and most likely will end up either burned or rotted, releasing the carbon as CO2. Recycling helps this, of course.
Maybe we should start to build more long-term things from timber, likely we would fire-proof them well. But steel, concrete, and plastics are still much easier to use for long-term structures like large buildings, bridges, roads, etc.
If it's used to produce paper, or wooden packaging, or for making chopsticks, etc, it would likely not. All these things are expendable, and most likely will end up either burned or rotted, releasing the carbon as CO2. Recycling helps this, of course.