This is exactly what was done with salmon in the Great Lakes to try to control the alewife population, and it is still being done today. There are probably other examples as well.
See Yellowstone 2015/2016: Fisheries biologists dumped Rotenone into Soda Butte creek to attempt to kill of non-native Brook trout. It will basically kill all fish and invertebrates in the poisoned area and will definitely have some long-term effects. I really do hope it works out, because Soda Butte is one of my favorite trout streams out west. It will be interesting to see how long it takes to rebound from the poisoning, and if it really does kill off all of the brookies.