Sure, a newly planted forest consumes CO2. The forest gains mass, and the mass gain is proportional to the total amount of CO2 that was consumed.
I've written about this before, and now I will write about it again, because I don't save links to my old posts — when they scroll off the history, the fart smelling stops. I read several papers about this subject specifically because the "question" comes up here frequently, usually in the form of someone insisting that young trees sequester more carbon than mature ones. This sounds perfectly logical, but in fact it is mostly false.
The trees of most species can use considerably more carbon in their old age than when they are young. There are multiple reasons for this, but the two most important ones are as follows: Photosynthesis is what's driving the use of carbon, and larger trees can do more of it; and all growth occurs in a thin layer below the bark called the cambium, which is larger in mature trees.
The other major factor in forest carbon sequestration is whether decomposition is aerobic or anaerobic. When it is the latter, most of the carbon is lost into the air during the decomposition process. When it is the former, most of it goes into the soil. This in turn is based on the presence of water and the rate of growth. Rainforests tend to have both lots of water and high growth rates, so they build deep layers that tend to decompose anaerobically.
Any forest that is mature and in equilibrium has constant mass.
Forests are not closed systems, so they don't have to be in equilibrium. And in fact, they generally are not. Because the byproducts of their decomposition tend to produce arable soil, and trees have evolved mechanisms for surviving or regrowing after fires, they tend to grow until something happens to them. Usually, that's us.