The displacer has a fixed volume. If you hold a rock or an aluminum basketball with the top below the surface in a water tank the same amont of water is displaces as if it were on the bottom of the tank.
The displacement is the same. The question was buoyancy. The buoyancy is different because the density of the displsced liquid gets higher as you go lower (for instance if there is a water layer under gacoline). It is probably a pretty small but calculatable effect that may have little practical meaning.
