Possible but unlikely i'd say.
3 other options:
1) try the CDR in another make of drive (i've seen laptop drives not be happy reading disks a full 3.5" drive would)
2) try someone like Ontrack (
CD-ROM and DVD-ROM Data Recovery - Ontrack Data Recovery), although it's £££
3) lastly, try one of those CD polishing kits on it (if it's skipping as a result of scratches etc rather than the organic dye decomposing)