Burn in procedure?

No,
You can burn interconnects even aside from the amp or components:

1. Connect the ends of an interconnect to the DMM test leads using an aligator clips
2. Connect one test lead to the HOT prong of the AC recepticle and another test lead to NEWTRAL prong of the AC recepticle

Here you go: you'll burn your interconnects insntantly!

For interconnects, and speaker cables, consider a "professional" accelerated burn in process lasting approximately three days, for about $20 to $30 at cableburner.com
I found that the gadget used by George Saubon produced a positive performance change, even on interconnects that were already well used, and already had been burned in specially by my using a special CD-R from Purist Audio Design.
For power cords, there is an inexpensive plug that allows you to "exercise" your power cord to the max. See archived past discussions about power cord burn-in for more detail on that topic.

Well, to burn in gear w/o buying aftermarket gadgets as listed above, with cables it is my understanding you need signal / current at least going through that cable, obviously. If you are burning in an interconnect on your CD player, you need to have the CD player running, obviously, but I do not believe you need the preamp on and I see no reason to need the amp on. I think you get the picture. For electronics, you need signal going through the piece you want burned in. EX. If a CD player, run the CD player; if a preamp, run a source to the preamp and have the preamp on; an amp would need all three on. Again, you get the picture. A side note, on an amp, does the volume level matter??? That I don't know.

Brian