Yes, this is quite possible to distinguish between a raw egg and a hardboiled egg by spinning them on the surface of a table. In the raw egg, the yolk and white are loosely bound. When such an egg is spun, its liquid mass experiences a centrifugal force which pushes the liquid mass away from the center. The increased mass concentration near the corners of the egg increases the moment of inertia of the egg. Similarly, in the case of a hardboiled egg, the mass inside the egg (yolk and white) is rigid and hard and when spun, they don’t move away from their places. Thus the moment of inertia undergoes no significant change. Now we know that torque is proportional to the moment arm
τ = IαTherefore, increasing the moment of inertia will increase the torque and vice versa. So when equal torques (rotational forces) are applied, the raw egg due to its larger moment arm will make fewer revolutions as compared to a hardly boiled egg (see the above equation). Therefore, it is possible for a person to distinguish between a raw egg and a hardly boiled egg by spinning them on the surface of a table.