ouch yeah...at least, not if the user of that code hasn't used it to register theirs. THey can only identify your regis code if it hasn't been claimed already. At least, I'm assuming so...
I think it's worth the 20, but it's not worth 20 per computer. I think they should've just made it so you still get one code and can register it on more than one computer...I got it registered on my parents' computer which was the only one in the house with internet, and then Dad got me my own computer...now I can't register GM on my machine and I'm not gonna pay another 20$ that I don't have.