Only if there is a very large lake at the bottom. If that lake doesn't exist then you have to build it at great cost. You also lose a lot to evaporation if you do this.

The 3.6 GW Fenging pumped storage facility holds 53 thousand acre-feet of water. Lake Mead holds 28 million acre-feet of water to run a 2 GW generator.

Just because you're using less water to power a more efficient generator does not mean the water in the lake is any less susceptible to evaporation and less water from upstream to replenish the lake.

Where "very large" is still a lot smaller than the water requirements for hydro generation.

Large enough to replace all that water requirements, without making the lake levels so high that it impacts generation. Which is to say your lake at the bottom needs to have a large surface area when full - much larger than the lake at the top.