I wouldn't want the cords laying on top of the countertop.
Holes can be drilled in the countertop where you need them and put grommets in them to make them look nice and professional. Purchase the grommets first then drill the holes so you know what size hole to drill.
Another suggestion is to tape a label on the plug in side of each device. When you go to plug in or unplug, you'll know exactly which one you're unplugging! :) I do this in all situation where I have multiple plugs plugged in (by the tv, the computer, the sewing area, game area).