There is not a simple yes or no answer. It comes down to choosing products appropriate for the face fibers, dye system used and other construction factors of a rug. There are hundreds upon hundreds of possibilities. Olefin rugs with synthetic foundation yarns can be treated the same as a wall to wall carpet. With wool face yarns and cotton foundation and fringe, oxidizers, reducers, any type of bleach can weaken the fiber. Some dyes may bleed with water or any water based chemical.
It depends on the fiber - and if it is wool, it depends on if the rug has been chemically washed before coming to the store, which MOST have. But absolutely using spotters made for wall-to-wall on wool rugs will get you into BIG trouble. I like Perky spotter on wool - it's not as nuclear an option as many of the others. Lisa