If you make a bootable clone using either CCC or SuperDuper that will be a copy of the entire system. So if you boot from the clone it will be exactly the same as your system drive when the clone was made.
I use SuperDuper and I have it schedule to incrementally backup weekly to keep the clone current on a weekly bases. I think you can do the same thing with CCC.
By the way a Time Machine backup is not bootable. To recover with a Time Machine backup it is necessary for you to first install the operating system.