That’s not my understanding of it. Active and damping modes have nothing to do with flight control laws.
The CBT you have looked at is a little misleading, because active and damping mode refers to the hydraulic jacks in the flight control surface itself.
So, in normal flight, ELAC 2 controls the elevators through the green and yellow hydraulic systems. This means the hydraulic jacks in the elevator that are doing the actual pushing and pulling are the green and yellow ones, these are the “active” ones. The damped Jacks are controlled by the blue hydraulic system and act as a damping force or drag on the active jacks. This serves to smooth out the control surface movement much like the dampers in your car.
Only if ELAC 2 fails, would the blue jacks take over, because ELAC 1 is now controlling the elevators, and the green and yellow jacks becoming the damping force. A single ELAC failure would not result in a flight control law downgrade, and you would remain in normal law (had to look that up!).
That’s my understanding of the system, and am happy to be corrected if I'm wrong.
My advice to you would be to avoid CBTs at this stage and get a copy of the FCOMS instead.