Yes, rotenone kills the rainbow trout in the treated water - and all other fish (perch, brook trout, rainbow trout, cutthroat trout, etc.).
Rotenone is an odorless, colorless organic compound extracted from the roots of a native legume known as a Jicama vine found in South America. Before being refined and used in the United States for fish management purposes, it was used by native tribal members to kill fish for food purposes.
Rotenone will kill all animals that use gills to take oxygen from the water. This includes all fish, aquatic insects and amphibians. It disrupts the exchange of oxygen across the gill membrane, at the cellular level, and essentially suffocates the aquatic organism.
For the purpose of fish management in the U.S., rotenone powder is dissolved in a petroleum carrier that has a strong odor and turns white when it contacts water. This is so we can tell where it's applied and whether it is mixing throughout the water column. Rotenone and the carrier agent can only be applied at a maximum rate of 4 parts per million for fish management purposes and rapidly breaks down - depending on water temperatures and organic material. Usually, fish can once again survive in a water 2 weeks, post treatment.