Can areas already in another federal designation, such as wilderness or national conservation area, be designated as a wild and scenic river?

Yes. Congress has frequently added wild and scenic river status to rivers flowing through national parks, national wildlife refuges, and designated wilderness. Each designation recognizes distinct values for protection, and management objectives generally designed to not conflict. In some cases, wild and scenic river designations extend beyond the boundaries of other administrative or congressional area designations, thereby providing additional protection to the free-flowing condition and river values of the area. Section 10(b) of the Wild & Scenic Rivers Act addresses potential conflicts between the Wilderness Act and the Wild & Scenic Rivers Act and states, in cases where this occurs, the more restrictive provisions would apply.

Source
Interagency Wild & Scenic Rivers Council