Long term, the paper will decompose while sitting in the landfill and then release the carbon back into the atmosphere. Even temporary sequestration is beneficial, but I don’t know whether it is still a net positive once you factor in the resources spent growing the wood, mailing the paper, and transporting it to a landfill.
Many US landfills capture methane, since they can then profitably sell/burn it. I haven't seen anything about them capturing all the CO2 emitted, which would be much trickier.
