Have you tested this theory?
The capacitance is εA/d where ε depends on the material, A is the area and d is the distance between electrodes. Increasing the pressure will decrease d, decrease A twice and might do something to ε. Unless you have proper figures from the manufacturer, a small decrease in capacitance with pressure is a sensible guess.
The maximum voltage depends on d and the material. Increasing the pressure reduces d, but also (often) increases the breakdown voltage. Unless you have proper figures from the manufacturer, expecting the maximum voltage to remain constant is a sensible guess.
The other figures of merit are impedance at working frequency, maximum current, and temperature for 1000 hours of life. (1000 hours is far too short, so over specify the voltage by a factor of two to double the life, and over specify the temperature by 10C to double the life. Repeat until life time = mandatory guaranty.) It is really hard to guess what some extra pressure would do to these values, but you can be confident that the voltage and temperature markings on the capacitor wildly exceed those it will actually experience, and the whole idea of liquid cooling is to be more effective than air cooling.
How much pressure: every 10m of water get you an extra atmosphere of pressure. I doubt that the tanks are a whole 2m deep, and oil floats on water, so a sensible guess is less than a 20% increase in pressure.
In digital circuits, the capacitors are there to stop ground bounce. The capacitors were not selected for capacitance, and ±20% is often chosen because they are cheap. The figure that matters is impedance at some frequency. Often two sizes are fitted to cover a wide range of frequencies. The actual impedance has to be 'low enough', and as the components are cheap, adding plenty is often cheaper than experimenting to find out how few you can get away with.
In power circuits, the important number is maximum current. Selecting for this normally limits you to capacitors that have more capacitance than your circuit requires. The result is usually harmless, especially as modern (or ten year old) switch mode controllers have soft start built in to deal with large capacitive loads.
The only thing where pressure will make a clear difference is _after_ the circuit has failed. Abusing electrolytic capacitors causes them to create gasses inside the can until the can ruptures. The cans have been scored so they burst before the internal pressure becomes excessive. Increasing the external pressure will delay the rupture, and a liquid environment will do a better job of transmitting a shock wave to the rest of the power supply. This is entirely academic because the capacitor only ruptured because the power supply was already badly broken.
I can understand manufacturers voiding warranties as a precaution because they have not tested there components at 1.2 atmospheres. When I have looked for data, manufacturers did not know and did not care. The theory does not point to a clear and obvious problem, so the only way anyone is going to know for sure is to dunk a hundred power supplies, run them for two years and count the survivors.