No they don't. They need to be harvested and used for timber products, where the carbon can stay locked in for decades or longer. The land can then be replanted for more carbon removal.
Ideally you would use trees to make engineered wood products that replace steel and concrete, the production of which also release large amounts of CO2.
https://psmag.com/environment/young-trees-suck-up-more-carbo...
'Tropical rainforests, the revered "lungs of the planet," were once thought to take the cake when it comes to carbon sequestration. But a new study adds to a growing body of evidence that other types of forest may actually be better at sucking CO2 out of the atmosphere. Specifically it finds that young temperate forests may be more effective carbon sinks than are old rainforests.'
Filtration is good enough that it could technically capture everything.
Technically you could plant enough trees to capture all the CO2 as well.
The energy required to make all the filters and plant and maintain all the trees might be greater than the energy produced by coal though, and that is the issue.