Must aquatic and upland non-indigenous species present in the river area be removed once the river is designated?

No. Non-indigenous species need not be removed unless they are degrading other important resource values. Practical considerations, such as the effort or expense of eradicating a non-indigenous species and its importance (e.g., game species), should also be considered. This issue is generally addressed in the management plan.

Source
Interagency Wild & Scenic Rivers Council