I would think it would be like wondering how many people became fans of Lost in Space after the movie. Probably not many, they are such different beasts. "Does Uhura just sit there the whole time?"
Speaking of TOS vs TNG, I think TNG might work better for young people (God I sound old) because take away the dated FX, hairstyles and what not it still presents itself much like a contemporary show. TOS on the other hand is gloriously 60s which I think may be more challenging for them to relate to.