You’d have to sequester them such that they don’t biodegrade. This involves deep burial, difficult for a solid, or submersion, which means ruining a deep-sea habitat (and creating a carbon time bomb).
The cost of raw wood is not a big contributor to the cost of housing. The shortage of land where people want to live and are legally allowed to build is the biggest problem. Behind that, cost of construction labor.
The carbon in the wood used to build houses will slowly (or rapidly in the most unfortunate cases) release back into the atmosphere by various mechanisms.
