I tried this once with one of those WD "Passport" backup drives. Using USB 2.0, VM performance is total crap. Haven't tried it on USB 3.0, it should be OK.
However, on that same WD Passport, I did install a Linux OS through USB 2.0, it ran fine. Not quite as fast as the internal install, but not that much slower. If it's a Linux OS that you want to use, this would be OK, but remove your primary hard drive first, or your bootloader will be overwritten. At startup, press the ESC key (or whatever key allows you the choice of boot options), it should boot fine.
This can't be done with a Windows OS. You'll need either the eSATA or USB 3.0, and run through whatever VM software that you use.