Yes, they do....generally speaking, of course.
I have used many CD players of varying quality over the years.
IN GENERAL, the nicer the CD player, the better the unit responds to a nicer cord.
If you are using a cheapie CD player (say....under $1k), you probably won’t hear a difference.
When you start talking about $2K+ players with quality power supply(-ies), then yes, you can hear a difference. I don’t think you need to go overboard with the quality of the cord, but a couple-of-hundred dollar cord on a good CD player will be noticeable.
(It’s easily demonstrable with my Esoteric, Yamaha, Classe, modified Denon tube CD player, etc...)
Everything makes a difference on audiophile equipment, and CD players are no different.
P.S. Nice setup. Love the speakers!