Also desalinated water does not to be used the moment it is produced. One can run desalination facility at full blast during the day using renewable energy and at a lower or even trickling speed during the night using cheaper, often wasted otherwise energy from the grid.
The advantage is that you need a smaller desalination facility, as it can run at 100% duty cycle. Pumped hydroelectricity could do something similar, but why not have a go at removing the losses of converting back to electricity. (Then again, if you have an electric pump you already have most of the equipment required to produce hydroelectricity by running it in reverse, so pumped hydro might be better because it is more versatile?)
The drinkable water can be viewed by itself as "salty water + stored energy". If you produce it at any time where electricity demand is low/or production exceeds demand you store energy already produced, be it by nuclear or renewable power plants.
And then you can build the pumped-hydroelectric power station where it makes sense, not being limited to the coast line/big city being close.
Even if one lives on a desert coast there may be times where it makes more sense to purify and store water from say flash floods than desalinate it from the sea.
IMHO your idea may work if we think about some isolated location not attached to the grid and without some power plant running 24/7. No idea at which scale pumped hydroelectric starts to be viable.