Underwater rock conduit
I must admit that I was not well informed on the matter of offshore aquifers before reading this thread. Usually when I think about the hydrologic models I think of the water as a dynamic component of a system (snow, streams, moisture, glaciers) and not necessarily old water pockets somewhat trapped deep (and at the moment with no know perceptible input/ouput in the system). In line with those classical hydrologic cycle model.

I searched a bit and found this paper on physorg.org which led me to other reads on the matter.

Apparently there is substantial offshore freshwater aquifers, trapped undersea. Water from Pleistocene, which probably got trapped during the glaciations, while the mean sea level was much lower. When the ice sheet (ex: Laurentidian) receded, sea level rose and freshwater in charged aquifers would be somewhat trapped and sealed. Multiple glaciation during the Pleistocene would have enabled the process to cycle multiple time during the last 2.5 M year.

And yes - the related paper in Nature specify that some of those 30 inventoried undersea aquifers have an onshore connection (Perth among others is listed there).

This is pretty interesting but in my opinion there is not a ton of paper on the question. Yet I will keep this part of this (paleo!) hydrologic cycle in mind when such questions and discussions arise in the future.