Just guessing out of nowhere, based on my own IDE-ZIP100 memories with DOS:
Did you try booting the machine with a ZIP diskette in the drive?
I remember, DOS never gave a letter to the drive, but the diskette, when using the IDE ZIP100 drive.
Perhaps it's the same with OS/2. Leave the disk inserted, and restart. - Does it have a drive letter now?
The USB ZIP100 however, does indeed still assign you a drive letter, when inserting a diskette while the operating system is already fully booted.