I made my donation a bit more than two years ago, and if I received any acknowledgement - the only record I've got is a copy of my PayPal statement - it was no more than instructions about turning off the advertisements, so I'm not sure what serial # you're referring to.
My impression is that Bombich first began issuing serial #s when CCC changed from donationware to $39.95 shareware, and that was pretty recently.
Edit 1: And Mike Bombich is so cool that the instructions for turning off the ads was readily available on his Web site even to non-contributors.
Edit 2:
This is somewhat helpful, but I'm no less confused about whether I should or shouldn't have a serial #; next stop, e-mail.
Edit 3: While searching, I ran across this:
June16, 2003
Carbon Copy Cloner - OS X - Jaguar
How to create a second Boot drive in OS X.
Shareware utility by Mike Bombich - $5
Mac OS 10.2+ and Mac OS 10.1.2 thru 10.1.5
So CCC went from shareware to donationware and is now shareware again.
Edit 4: I just realized that I misunderstood your post and that you seem to have been in the same position I'm in, but this may help others in the same position.