Depends, as bcastner say if it were a removable drive i.e. a hdd on a removable hdd rack then yes. An external SCSI drive - yes.
You only have to tell the BIOS the boot device priority, then everything will be fine. If your BIOS supports boot from a USB device then an external USB HDD might work, not sure about this though coz i haven't much success over the endeavor.
Here at work, I have the system drive of one of my file servers on a removable HDD, which I also configured the unit to boot via an external SCSI HDD in the event that the system drive fails. Could have used raid but I had an extra SCSI card lying on my shelf so I just plugged it in and used that. Well I'm like that - use available resources first before buying something that's not on my inventory.
That's my take on the subject.