It all depends. Was there a ligitimate OS on your computer before you installed the illigitimate copy of XP upgrade? If not then you must purchase a full version of XP to be legal. Otherwise yes you can do that. Actually all you need to do is replace the authentication code in the OS and then do an activation (See MS KB article 328874). This way you don't have to do a full reinstall.
Al-
Nice reference to the MS Knowledge Base, wish more people used it.
Question for you though do you have an MCP #?
If not let me know I might be able to get you a Special number so you can access special parts of the microsoft website.