No, wood burning only releases the CO2 that the tree absorbed from the air during its lifetime, which was mostly going back into the air anyway if it rots. It's the carbon cycle, whereas if you dig up coal that's carbon captured by plants that got buried long ago, so it adds to the carbon in the atmosphere now. If you want trees to sequester more carbon you can cut them down and build stuff that will last a long time, and that leaves room for a new tree and carbon stored in a useful form.