This article is from the CD-Recordable FAQ, by Andy McFadden (email@example.com) with numerous contributions by others.
Generally speaking, no, though warnings have started to appear.
One proposed line of reasoning is that the lower reflectivity of CD-R media
causes the laser to work too hard. This only makes sense for players
with an AGC (Automatic Gain Control) circuit, in which the laser power
adjusts automatically. This feature is generally found in newer players,
because it's required for reliable playback of CD-RW discs.
It seems unlikely that a player with an AGC would fry itself while running
at a valid power level, unless the device were poorly constructed. In any
event, the reflectivity of CD-R is close to that of CD -- if it weren't,
CD-R would have the same playback compatibility problems that CD-RW has.
The laser shouldn't have to work any harder to read CD-R. It's possible
that some devices might "strain themselves" over CD-RW discs, but any
device built to work with CD-RW should be able to handle the media without
A more likely scenario relates to differences in physical dimensions.
One car dealer claimed that CD-R media is too thin, causing their 6-disc
changer to occasionally grab two discs and jam itself. On the opposite end
of the spectrum, some "slot-in" dashboard players will get stuck ejecting
a CD-R that has had an adhesive label added, because the disc is too thick.
It's possible that the players with warnings simply don't support CD-R
well for one reason or another. Rather than admit to poor construction,
the manufacturers are trying to make it seem like there's something wrong
with CD-R media.