Not necessarily. Wood doesn't decay in the same way in anaerobic conditions. The much older Mary Rose, Henry VIII's flagship, was raised in a well-preserved state from the bed of soft silt in which she lay.
About the wood: I don’t know why some wood rots, and some doesn’t. And I don’t know the temps of the waters where the ship sank. But, they have recovered loads of wood lost in the Great Lakes from the late 1700s to the late 1800s and they sell it for furniture. It’s quite valuable.