Is it possible and relatively easy to boot a 2013 MacBook Air from an external drive? Given a MacBook Air that's working but with dead display and SSD, can I use it as a desktop-only machine with an external monitor and external hard drive?

The guy at the Apple Store Genius Bar this afternoon told me I could install the OS on an external drive and boot from it, but I'm sure even Apple Geniuses sometimes make wrong assumptions?

If it is possible would a USB external drive suffice or would it require a drive that connects to the proprietary connector?

Also if it is possible, is it fairly straightforward?

(I am a technical/computer guy, but not a Mac guy.)
It should work, depending on the model of MacBook Air an external USB drive will be able to boot the system but it will likely be slower than an internal drive on the PCI/SATA bus. You should also have a Thunderbolt or mini display port for connecting a monitor. 

So it should work. Whether or not it will perform acceptably is difficult to say.