Does the preamp need to be on?
As @ozzy said there needs to be signal passing from the source to a load. Load is the Preamp in this case. Naturally the preamp would need to have the input selected for the CDP.
Could the preamp be set to the input the CDP is connected to and then be powered off? Depends on the preamp. Some preamps use relays or some other type of source switching device other than a mechanical input switch. do you know what you have?
As for break-in, burn-in, settle-in, what ever you want to call it, it’s not just the wire that burns-in. The RCA plugs need to burn-in. The dielectric, insulating material that cover the bare wire needs to burn-in, settle-in as well. The signal energy actually travels in the space between the wires through the dielectric.