Interconnect Break In?

I don't know, but my power cords had to break-in to sound smoother, why not   interconnects. Logically the gear has to be on for any break-in to occur. You know, the electrons have to find their shortest signal path and components have to settle in. 

I’ve pursued high end audio for fifty years. I have spent hundreds of hours comparing high end audio interconnects, speaker wires and power cords. Breaking is substantial and not in your head. 150 to 200 hours is very typical. I find a couple components I can have on… both ends. I have an extra system that I can put in wires and break in… I always go for the highest power end… like if I have phono stage interconnects I’ll use between the preamp and amp to break in. 

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.

@jasonbourne71 " What does change over time is the contact resistance of the connectors due to oxidation.” +1

Simple unplug-plug the same cable changes contact resistance dramatically! Always check your contacts under microscope of just magnifying glass, what you’ll see might shock you! Contact surface is another problem, often “gold plated” contacts are much worse than pure Cu, due to high resistive metal under it (Ti, Ni etc). I found recently couple of very good Rhodium plated receptacles and plugs, showing very low interconnect resistance, and no scratches after use! Remember as contact established by two parts, thus these parts should match in terms of plating metal, ideal metal pressure etc. 

Cables from resistance standpoint are getting worse with time. Dielectric (bad one) hardens and changes Er/TanD after few years of use, which significantly degrades phase velocity flatness across audible frequencies. The lower dielectric constant is, the better! Shorter audio cables have less audible sensitivity to phase velocity than longer ones. 

I’m glad I read this thread because it reminded me to check all my cable contacts. It’s been a while since I’ve done that. For whatever reason I’m not one who can hear differences between cables, except in extreme cases, like interconnects or speaker cables that are very long and too high in resistance. Another case was some cables with a little transformer built in to convert pro level output down to consumer level. Those things sounded horrible. They also measure poorly. Another thing that can sound really bad is using a y-splitter. Very obvious stuff. Comparing two interconnects of any cost that are both meeting basic criteria and suitable for the application has proven mission impossible for me. I also can't tell if it's been broken in or not.