No, i don't believe that will work. I understand your theory, but it is flawed (saying that with love). See, if the data on the CD is unreadable, why would nero be able to read it and the OS not? If you burn the CD you are going to run into the same problem, when it hits that portion of the CD the data will be unreadable. And i bet Nero will do a data check and see that the area is scratched anyways.
If this is new RETURN IT. If you are impatient and have other routes to go, then borrow a CD of the same version from a friend and just use your purchased CD key. My vote would if this is a legit CD (which i have a feeling it isn't) then it needs to be returned for a new one.