This article is from the CD-Recordable FAQ, by Andy McFadden (email@example.com) with numerous contributions by others.
Yes and no. Your eyes can tell you that the disc is different, but the
laser in the CD player can't.
A "black" disc, popularized by the tint added to Playstation games, has
had color added to the polycarbonate layer. The tint looks very dark to
the eye, but so long as it doesn't absorb or disperse too much light in
the laser wavelength it won't interfere with disc performance. If you
hold the disc in front of a light, you may discover that your "black"
disc is actually very dark red.
Some people have suggested that, by blocking other light, the coloration
enhances the performance of the disc. This makes about as much sense
as drawing around the outside of the disc with a green magic marker (a
popular myth from the 1980s).
If you find that "black" discs work poorly or especially well, you haven't
discovered anything different from what most owners of CD recorders know:
some discs just work better than others. The tint in the plastic isn't
likely to be involved.
(Some users have done some fairly careful testing, and found that "black"
audio discs sounded better than non-black discs from the same manufacturer.
I haven't seen a controlled double-blind study that reached this conclusion,
but there is anecdotal evidence to suggest that the colored polycarbonate
causes the discs to sound different.)