No. Some of the carbon can end up being stored in the soil:

https://extension.psu.edu/how-forests-store-carbon

Or alternatively, wood can be used for increasingly complex construction, for example this wooden skyscraper:

https://www.thetimes.co.uk/article/berlins-woho-wooden-skysc...

Lastly, just increasing the carbon stored in living mass may be vastly beneficial.