The advantage is having it built out of concrete. But because concrete has compression strength, not so much tensile strength, you need to store negative pressure not positive pressure.
The available pressure at 700m underwater is considerable. There's no equivalent reservoir of high-pressure fluid on the surface (the atmosphere is at a much lower pressure, obviously).
(The pressure difference in submarines is notably much bigger and more troublesome than the pressure difference spacecraft in a vacuum need to resist.)
So surely it's the high pressure at depth that's the attractive resource here? Pumping a gas into a cavern could offer a positive pressure solution, and I'm pretty sure that's been proposed already.
You get exactly the same pressure from traditional pumped storage of the same height. (Well, ignoring the tiny density difference between salt and fresh water)
That's not an advantage to having it underwater. In an above water version using a 700m mountain, the vessel to hold the water would use far less concrete. It's basically a swimming pool.
Not a swimming pool, but a reservoir, and there are already many used for pumped storage. The problem is that you can only do that where the local conditions allow it: you need space for the higher and lower reservoirs, space for laying down the pipes, and enough cheap water to refill the reservoirs (because of evaporation).
The possible big advantage of this solution is that it could be built wherever the sea is deep enough and partially use the existing infrastructure of offshore wind farms.
