No. RJL System Cleaner does not use license keys, serial numbers, activation codes, or online activation of any kind.
When you register, you receive a download link for the registered .exe. You replace your existing file with the registered one. That is the entire process. The registered .exe is a separate build with all premium features enabled and the closing splash screen removed.
This means there is nothing to lose, nothing to forget, and nothing to re-enter after a Windows reinstall. Just keep a copy of the registered .exe and use it wherever you need.