After looking at this question - Source of water for the Great Artesian Basin in Australia one would like to know whether there are any underwater rock conduits that transport fresh water across seas in the world. I have not come across any in my search, but maybe there does exist that I am not aware of.
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.
From a purely hypothetical point of view, it is very unlikely that a submerged aquifer could carry freshwater underneath a marine environment. Salt water being more dense that fresh water would seep into the aquifer and displace the freshwater. The saltwater intrusions into freshwater aquifers in coastal regions across the globe is proof of this behavior.
A possible but improbable scenario for your underwater rock conduit might be to have a sealed artesian aquifer with significant pressure gradient (perhaps limestone/dolomite bounded by shale) whose source is nearby mountains submerged by sea water in a valley.