Yup and Nop
You are correct unless it is a tube chassis car, Dragster or tube chassis altered, then it has to have some sort of current chassis sticker, even if you are running 12 second times. Other than these exceptions, you are correct.
You might find that most local tracks will ok your use of a tube car without a sticker if you are running slower than 10.01, they are in my neck of the woods here in Michigan.
Bruce