We have a big natural pond with Koi and wild ducks. The ducks cause problems as they make the pool filthy, they live on it so they would, even though the pond is naturally draining and filling from a stream so continuously cleaned the wild ducks seem to cloud it up so it is not ideal for the fish.

I would keep the two separate especially if a man-made pond. Our domesticated ducks need their smaller pool refilled every week or it gets yucky, so I doubt that any fish would survive due to the lack of oxygenation and the fact that the ducks eat all the vegetation needed by the fish. Refilling also means we have to de-chlorinate the water before any fish.