Under sea pipelines for a variety of depths, pressures and capacities are a solved problem, courtesy of the oil and gas industry.

These pipelines have some inner pressure. The idea is here however that a pressure differential is used to drive a turbine. The greater the differential the more energy. The engineering challenges are not really comparable.

The engineering challenge is more comparable to submarine design. Nuclear submarines go down 500m and even the navy deep submergence rescue vehicle http://www.navy.mil/navydata/fact_display.asp?cid=4100&tid=5... is going 1.5km deep only with its tube design. Compare this with really, really deep dive designs like https://en.wikipedia.org/wiki/File:Trieste_nh96807.svg with a sphere observation gondola.

The US Navy's DSRV's you referenced do not have cylindrical pressure vessels. The cylindrical external hull encloses 3 linked spheres that are the actual pressure vessel. BTW, the DSRV's were retired several years ago.

Seems to me that if you use compressed air to displace water within the sphere, you could actually store more energy this way... That would require the air to drive electric generators when the sphere is being filled with water though.

Once you start compressing and decompressing air you get a lot of heat loss though, that I would imagine isn't as much of an issue when you're just pumping plain water back and forth

The paper cites a depth of 700 meters too for either system. Compression happens to be concrete's best operating mode.