Well a label on a cd shouldnt really harm playback, but it is dependant on the device that is playing the disc and how it is setup.

Tray load devices should have no problem at all because the disc stays in the tray quite well.

Portable CD players usually have only a very small contact point in the middle, which would only harm playback if the the cd became very unbalanced which is quite hard to do with a uniform logo placed well.

slot load players such as car cd players can have a problem with labels if the label comes loose anywhere, once a bit of it comes up from the disc surface, it starts to not insert and eject well, and can be easily unbalanced.

A Label with good quality glue, and stuck onto the cd with one of those cd labelling hand machines ( theres a bunch of them ) perfectly centered should cause no problem at all.