I've been able to get compacts to work with CDROMs, even with System 6. A couple of problems seem to be common:
1) Other than factory-pressed media tends to be unreadable in older drives, or readable only with errors. Some brands of CD-R media might work in these (but don't count on it), but CD-RW is pretty much hopeless. The reflectance is just too low to operate in a drive that hasn't been specifically designed for CD-RW support.
2) Some older drives may have difficulty with 700MB discs. The track-following servos may have insufficient margin to handle the slightly tighter track pitch.
3) SCSI termination/power issues tend to frustrate. Compact macs can't supply termination power, so the external drive has to provide it.
4) When using a CDROM drive with System 6, it is absolutely essential to use Desktop Manager to prevent futile attempts at desktop-rebuilding.
5) If audio support is not needed, CDSunrise is a gem of a driver. It's small, for one thing (ideal for resource-constrained compacts), and it seems to work with just about every drive.