No, CCC will exclude the Backups.backupdb folder during a backup task because Time Machine backup folders contain Apple-proprietary filesystem devices. Apple does not document a procedure for making copies of Time Machine volumes.
Backing up Time Machine sparsebundle disk images
When Time Machine is configured to back up a Macintosh to a network volume (such as a Time Capsule device), Time Machine stores the backup in a sparsebundle disk image. CCC can copy these sparsebundle disk image files without any special configuration; simply choose your network volume as the source of your CCC backup task. In fact, CCC quite capably copies only the bands within the sparsebundle that have changed, so you can add CCC to this type of setup for a second tier backup to an offsite network share.
Note that CCC will exclude the Backups.backupdb folder at the root level of a volume by default. If your source volume has a folder by that name, and you want CCC to copy sparsebundle disk images from this folder, you can choose Choose a folder... from CCC's Source selector and choose the Backups.backupdb folder directly to configure CCC to back up the sparsebundle disk images. Note that the only items in a Backups.backupdb folder that CCC will copy are sparsebundle disk images. Other folders, e.g. local Time Machine backups will be excluded. Further, CCC will only consider sparsebundle images for deletion in a Backups.backupdb folder on the destination. Other items in this folder on the destination will be protected from deletion.
Lastly, please note that no application can access the contents of a sparsebundle disk image file while that disk image is mounted or otherwise deemed to be in use. For example, if your Time Machine backups are currently running and backing up to a disk image, CCC will not be able to copy the disk image file, rather it will get an error that the files are in use.