This article is from the CD-Recordable FAQ, by Andy McFadden (firstname.lastname@example.org) with numerous contributions by others.
In general, no, but it appears that some stand-alone consumer audio CD
recorders write one. The Recorder Unique Identifier (RID) is a 97-bit code
recorded every 100 sectors. It is composed of a brand name identifier,
a type number, and a drive serial number. Recorders such as the Philips
CDR870 write the RID to discourage distribution of copyrighted material.
Windows will show something like "Volume Serial Number is 4365-0FED".
There does not appear to be any way to control this. Some have suggested
that the serial number is generated based on data found on the disc,
similar to the way that audio CDs can (mostly) be uniquely identified by
the number and durations of the tracks.
On floppy disks and hard drives, the "serial number" is generated based
on the date and time when the disk is formatted. The four bytes are:
1. month + seconds
2. day + hundredths of a second
3. high byte of the year + hours
4. low byte of the year + minutes
(From www.zdnet.com/pcmag/pctech/content/solutions/uu1508a.htm, which no