Yes, but forests capture carbon quickly until the average age of the trees starts increasing. So zero to 50 years is good, but after that things really slow down. The amount of wood becomes relatively constant.
So slowly, very slowly leaves fall/get eaten by bugs, break down, and get absorbed by new trees. But there is a net gain, just a very slow one. Then things like continents collide, mountain ranges come and go, and significant biomass gets buried and under pressure and time turns into oil/gas.
So for scale we could cut down all trees and bury it and take 638 gigatonnes out of our ecosystem. Not sure of the average tree age, but assuming it was replanted we could likely repeat that every 20-30 years.
The annual oil consumption looks to be around 36 billion barrels. Each weighs around 300 pounds. If my conversion is right that's about 4.9 Gigatonne.
So burying all trees every 30 years would be about 21.2 gigatonne a year or enough to offset all oil consumption AND decrease our current levels to pre-industrial levels.
Or we could just use less oil.