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You can in fact! Pumped hydro is already the cheapest form of energy storage - about 95% of all energy storage is pumped hydro. We can't build more pumped hydro because it's not feasible to build enough dams. (We've used up the best locations)

The US Gov has studied plenty of research showing that underground pumped hydro is cost effective and obviates the need for dams. (See my white paper here: https://github.com/syllable-hq/uphs-feasibility-study)

So startups like Gravitricity (and Terrament, my startup) are innovating on what is already well-researched territory.

Anything involving dams typically also has to involve water release schedules, which at least in some parts of the western US will produce some of the most vicious political battles you can imagine.

Same concept, but the tl;dr is that no, you can't, unless you're talking hydro from a dam in a good location. It's not just a not-so good idea, it's an orders-of-magnitude-awful idea when you compare it to just about any other form of energy storage per dollar.