No, Final Draft 13 uses an entirely different copy protection system than its predecessors. The email address and password you created to sign in to FD13 is good only with FD13.
If you've purchased FD13 and are having password issues, you can reset your password HERE. The link to the password reset is towards the bottom of the page.
FD12 / 11 / 10 still require your Customer Number.
10074
https://fd.support/48zqX4S