Yes, the magnetic force of Neo magnet can penetrate a wood with ordinary thickness to achieve the function of fixing and suction. However, there will be some loss when the pull force work through the wood, and suction force will be relatively reduced. If your magnet needs to work through wood, you need to choose the one with stronger force.
For very thick wooden boards, the magnetic force is decrease a lot after passing through the board. Therefore, when packing large pieces of powered NdFeB magnet, hard thick wooden boards are often used as spacers/gaskets.