Chickens don’t swim. If you toss them in a pool or pond they will float but if the edges are steep they can’t get out. It has to be shallow enough that they can walk out. If it is really hot they may stand with their feet in water to cool off, if the water is cool, but they will not take a bath in water. Chickens take dust baths, scratch shallow holes where it is really dry and wriggle and scratch to work that dust into their feathers.
Chickens need clean water and they don’t care where they poop, plus they are highly likely to scratch stuff into that pool. I’d think you are likely to have a dirty water how-do-I-keep-this-clean nightmare with that pool. As long as you don’t have ducks or geese in there I would not put that pool in the run.
