I noticed that there are a growing number of abandoned stacks of this type:
I wonder if they are physically strong enough to hold water, for use in pumped storage:
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Those aren't "smoke" stacks but cooling towers designed to let hot air rise and expand optimally.
These things are typically 200 m high. Static pressure of 200 m of water is pretty high.
They were never required to be water tight so they will leak. In fact towers are open at the bottom to let air in and rise inside. So to start you would need to seal that up. Sealing a retrofit patch to an adequate level that it'll keep that water in is very difficult. Getting waterproof concrete is usually done by poring the the entire slab in a single go to avoid leaky seams.
Cooling towers are designed for forced /induced draft cooling purpose, no big loading other than self weight and laeral wind forces.They would not be efficient pressel vessels holding water for likes of 200 meter water column height of Seco Rancho/CA.
If utilization of the twin towers is the main aim then alternate new big project features can be meaningfully defined i.e, if at all there is some scope for its implementation. Structural engineering strength,stiffness and stability for building a water reservoir around the towers is required as it is possible to design/model test/proto build. Much higher augmented capacity with efficiency and low unit power generation cost is possible with the stacks as external pressure vessels.
If water pressure acts on all four sides of stack, shell bending can be significantly reduced due to cancellation of equilibrated surrounding symmetrical forces.
The volume of water contained in the reservoir would be very high compared to inner stack volume. The turbines could be placed inside the stacks for potential power augmentation benefits.
A similar concrete filled very thin shell reticulated structure can be built around as a surrounding external wall /fort/dam/reservoir at a very low cost, not as a dam structure whose weight need not fall in the middle third for civil dam stability.The shape of meridian and generators can be further optimized by Form-Finding design principles. This is the principal new cost element here.
The present sketch/description is inadequate to explain all features due to novelty of design proposal made here.
Typically the walls on these stacks are very thin, less than 6 inches and their geometry provides the strength. They also from what i remember are typically build using wire mesh, not rebar on their structure though I could be wrong. If that's accurate, they would not be particularly stable for hoop pressure. They're designed for gravitational loading primarily.
Short answer, not likely.
Ironically, these could probably hold quite a bit of water. Probably not to the top, or even to the narrow part, but quite a bit. They're designed this way so they will work even without a fan at the bottom, the heat alone moves the water along and up the tower. They're also not made with curved members, but a bunch of straight beams inside the concrete:
Since they're so freakishly tall, those towers need a lot of beams with a lot of strength to hold up the high height and massive weight of the large towers. Cutting the towers to a shorter height, the beams wouldn't have to hold a lot of unsupported concrete weight on top, and that extra strength could be used to ... hold water. Depending on the size of the beams inside (the concrete can hold a lot of compression, but the actual pressure holding would be from the beams inside), quite a bit of pressure could be retained. You'd need to get a professional to review the actual tower, but the idea has merit.