What connection does the external hard drive use? There is (probably) nothing preventing you from installing the game on an external drive, but playing off one may cause performance problems. I'd guess a USB 2 drive would have issues, while USB 3 should be fine (but I've never tried playing a game off an external drive, if you don't count SCSI drives in an external enclosure).
You might be better off just keeping the saves on the external drive, and installing the game on the systems you will be playing it on. There are various ways to backup your saves to the external drive, or get Windows to redirect the game so it saves there directly, or even to sync the saves online using Dropbox, etc.
