I had the top of a white Oak tree fall into a clients small pond. Within a week (before the top was pulled out of the pond) the water turned black and it smelled bad, like a sewer. The pond, around 1/10 ac has an aeration system in it. No dead fish were seen, but that doesn't mean that scavengers didn't clean them up. It took about 3 months for the water to clear up somewhat, and at that time a minnow trap was put in the pond. FHM, Papershells and some BG YOY were observed, so not everything died.
I think it's on a case by case basis, and all depends on the water volume and the amount of tannic acid. Aeration might have played a role in it too.