Do Macs store a serial number on the disk?
Apparently the only ways to find out a Mac's serial number (if you don't have the Mac physically present) are:

When you had the Mac, you:


Registered it with Apple (check your support profile at apple.com)
Ran and saved a copy of System Profiler's output


Without the Mac:


Have a sales receipt from a retailer that puts the serial number on their receipts
Purchased it from a retailer that keeps track of serial numbers
Find the box the Mac came in


Thankfully, after I posted this question, the buyer was able to find the original box, which gave him the serial number.

But the actual answer to the question is: No, Macs do not normally store their serial number in a disk file.