On page 2.9 of the Apple IIc Technical Procedures, Apple IIc Diagnostics, the second sentence states that you can boot from the external drive in order to test that drive.
However, if you have an Apple IIc with the logic board upgraded with new ROMs and you attempt to boot it from the Apple IIc External 5.25" Drive, you get the message "AppleTalk Off-Line".
New or upgraded Apple IIc systems configure an Apple IIc External 5.25" Drive as a second drive, which cannot be used for a boot, as in the Apple IIe. Typing "PR#5" will just cause the system to hang, since the External 5.25" Drive is now considered to be Drive 2 of Slot 6. Typing "PR#7" will produce the "AppleTalk Off-Line" message.
You can, however, boot such a system from a 3.5" drive with a "PR#5" because new or upgraded Apple IIc systems configure the 3.5" drive as a first drive, Drive 1 of Slot 5, which can be used for a boot, as in the Apple IIe.