It does sound clever at first glance. It caught me at first, too.
The problem is, your fresh water is now several hundred feet below the surface. To raise it up to where you are, you need pumps to push up the same exact pressure differential that you got by putting the membrane so deep. And if you need to do that anyway, just use surface level water and pumps for ease of maintenance and access.
There was a startup pursuing a test setup using an oil derrick of Santa Barbara if I recall. These guys[1] were proposing a different system (basically providing fresh water to an underwater habitat) however the paper goes over the basics pretty effectively.
The problem is, your fresh water is now several hundred feet below the surface. To raise it up to where you are, you need pumps to push up the same exact pressure differential that you got by putting the membrane so deep. And if you need to do that anyway, just use surface level water and pumps for ease of maintenance and access.