Answer:
No. CC offers its licenses, code, and tools to the public free of charge, without obligation. You do not need to register with Creative Commons to apply a CC license to your material; it is legally valid as soon as you apply it to any material you have the legal right to license.
CC does not require or provide any means for creators or other rights holders to register use of a CC license, nor does CC maintain a database of works distributed under Creative Commons licenses. CC also does not require registration of the work with a national copyright agency.