Right, legally the Cowl that the Tag is attached to, is the car.
Cowl tag isn't the issue. It is the VIN tag that can not be removed, or altered under federal law. You can buy a cowl tag with any options you want listed on it and attach it to the car along with a counterfeit window tag that lists any rare options and motor combination you want. This is legal but frowned upon by purists.
For the record there is nothing special about an SS in the full size car. It is a style option not a performance option. You could order an SS with a six cylinder and a PowerGlide. An SS means you got a two door Sport Coupe Body with bucket seats and chromed trim; that's it.
You could order a light weight two door 1967 Biscayne sedan (post car) with a 427 engine, four speed, heavy duty suspension, a 12 bolt rear with a posi and beat up on Camaros or Chevelles; but it won't have the shiny trim stripes or SS logo.