Meanwhile in Germany:
Yes, they are part of the water cycle, sometimes collecting water from a significant area, but usually not. This is the upper reservoir of our largest hydro storage plant:
Rain is only collected over the area of the reservoir, and it would only fill up a few centimeters on a rainy day. In fact, the water evaporates quicker than that so a lake would never naturally form in this location.
Are all hydro storage like that though? It doesn’t seem too outlandish to think of a hydro storage plant that is also fed by a river