Well, it isn't ideal, and it won't be fast, but it will work just fine. USB 3.0 is plenty fast for a mechanical drive, but going through the USB controller hurts latency. Load times will be slow.
All those disadvantages aside, it will work. A lot of hardware reviewers keep their Steam libraries on external drives so they don't have to download their games onto every new system, so there is precedent for what you want to do, and if it works for people testing high end hardware it will work just fine for you too.