I have investigated this a little bit and I “think” that this is actually an incorrect setting in the model desriptor for both Copernicus DEM products. In Copernicus30mElevationModelDescriptor.java for example, the getNoDataValue() function returns a value of 0.
This has the effect ultimately of clipping out all marine data where the elevation is (legitimately) 0.
I agree that it would be might be useful to have this configurable, but in this instance, the model descriptor appears to be incorrect.