Yes. They can.
I was watching a documentary on one of the discovery-like channels; they were talking about the Library of Congress' media center out in Orange, VA; where they're currently archiving all analog content to digital and store a lot of stuff.
One of the things they showed was various CD's that had failed as a result of laser-rot or some kind of chemical breakdown. They had two of the same CD, both pressed at different times and from different factories. One disc looked flawless, the other looked like all the coating had flaked off, so there was nothing reflective left on the disc.
A scratch on a CD, depending how bad it is, usually causes the CD to skip, to repeat the same segment, or cause slight distortion; but only where the scratch is.
I've recently gotten in to LaserDiscs, which can suffer from "laser rot" from the glue oxidizing (Laserdiscs are actually two discs glued to a metal substrate). It affects an entire disc or just one side of a disc. But as I stated, that's a result of the glue holding the disc layers together causing oxidization. CD's aren't layered like a laserdisc, however, there is still something that has to bond the reflective substrate to the plastic disc.
One of the videos that shows the effect of laser-rot on laser discs talks about the loss of ability to play digital tracks. The rot causing such massive corruption in the digital stream that you get really scratchy/distorted audio.
Without actually hearing what the distortion is, it's difficult to say if it's a CD breakdown or a scratch. Usually, if the CD is failing, you will easily be able to tell. If you don't see anything wrong with the disc other than the scratch, well, then it's possible the scratch, when combined with the speed at which a CD spins, is causing that one track to not play properly.
I've got CD's that are 30 years old that are still fine. I've got some that are 10 years old that have the reflective layer flaking off. Much like laser-rot on laserdiscs, it's kind of a crap-shoot.