Cells consist mainly of water and the compressibility of water is very low. Wikipedia states:
The low compressibility of water means that even in the deep oceans at 4 km depth, where pressures are 40 MPa, there is only a 1.8% decrease in volume.
This means that the pressure alone does not affect the size of the cells much. However, the pressure affects the cells and the metabolism of organism living in extreme depths in other ways:
Under pressure, the folding and unfolding kinetics of proteins can change drastically. Which means, that the protein structures may need adaptation to great pressures.
Under pressure the fluidity of the cell membrane lipids changes, requiring adaptations in membrane lipid composition.
In conclusion, I would say that the pressure in the deep sea does not directly affect the size of cells but rather their metabolism.
Edit: I just saw the second part in the heading of your question ("and can they survive in shallow water?"). Again, I'll quote Wikipedia:
The extreme difference in pressure between the sea floor and the surface makes the creature's survival on the surface near impossible;
The reason for this is that pressure works thermodynamically in many ways similar to temperature: As explained above, changing the pressure significantly alters reaction kinetics and phase transitions. Thus, the whole metabolism has to adapt to increased pressure (similarly to the adaptation to increased temperature).
However, at least some deep sea creatures seem to be able to adapt to surface pressure if the transition is not too abrupt (from the same wikipedia article as above):
A marine biologist, Jeffery Drazen, has explored a solution, a pressurized fish trap. This captures a deep-water creature, and adjusts its internal pressure slowly to surface level as the creature is brought to the surface, in the hope that the creature can adjust.