No. Copying a Time Machine backup volume with anything other than the Finder is not supported (by us, nor Apple); CCC specifically disallows copying anything to or from a Time Machine backup volume. Apple's recommended procedure for copying a Time Machine volume is documented in this Apple Kbase article.
Can I use CCC to restore content from a Time Machine backup?
Generally, no. If you want to restore content from a Time Machine backup, you should use Apple's Time Machine interface for that purpose. If you see a Time Machine snapshot in CCC's Snapshots table, however, you may restore files from that snapshot.
Can I use the same backup disk for both CCC and Time Machine backups?
Yes, you may use the same physical device, however you should created dedicated volumes on the device for each backup.