It depends on your Motherboard (MB).
First of all, your external HD must have a bootable OS.
I am assuming the external hard drive (HD) is connected to your computer thru USB.
If the BIOS allows booting from USB-HD, then replace HD-0 (your primary HD) with USB-HD in boot sequence. Then the computer will boot from the external HD. Choosing ?Boot from other device? will not work.
Refer to your manual. Otherwise, check your MB manufacturer?s website whether the latest BIOS flash takes care of your concern.
If it boots, it will be REALLY slow.
The primary purpose of an external HD is to back up or for extra storage.