The short answer is it won't work. The long answer is related to the dissipation of pore-water pressures under dynamic loading. If you have experience in a soils lab, consider what happens when you run a Proctor Compaction Test. As the moisture content is increased towards optimum the degree of compaction increases -- but at moistures above optimum the degree of compaction decreases for the same energy input. At several points above optimum you will see the sample begin to bleed out excess moisture. If you try to compact a fully saturated sample, all of the energy is transferred to the water (an incompressible fluid).

I agree with TimC, it won't work. Additionally, you need to look at the mechanism for compaction, i.e. energy transfer. Basically, soil compaction takes place because of the transfer of the kinetic energy of the head into deformational energy of the soil. You won't be able to develop much kinetic energy. First, if you lift the compactor head outside of the water then most of the kinetic energy will be dissipated upon impact with the water because of water’s surface tension. The head might even bounce if it drops at the right speed. (I’m assuming a flat bottom to the head.) Second, underwater you will not develop much kinetic energy. Friction with the water and buoyancy will greatly hinder any development of kinetic energy and/or dissipate any previously developed. Put simply, non-streamlined things don’t move quickly through water and anything streamlined won’t be good for compaction.

Imagineer

An additional effect will make the transfer of energy to the sand inefficient - the water will flow around the face of the "hammer" and push surface sand out of the way as it approaches.  Have you ever tried to hit something underwater with your flat hand?  Try it and you will discover that very little force gets into the object you strike.  Also, try hitting the bottom of a lake or beach, you will see that much of the "soil" is pushed away and you are left with lots of muddy water.