I think the oxygen in the tree materials is already combined with carbon in the form of CxHyOz hydrocarbons, where x,y,z = atoms of the respective atomic species.
Burning cellulose (poly-C6 H10 O5) to CO2 and H2O would require (for each molecule): 12O (for 6CO2) and 5O (for 5H2O). This is a total of 17O.
Cellulose contains only 5O, so 12O (or 6O2) would be required for a full stoichiometric burn of cellulose.
Burning that carbon to CO2 requires oxygen, which will deplete the atmospheric reservoir to some degree.