Just because it has a USB C port doesn't mean that's what it's used for. This port is specifically used for "servicing" (and occasional side loading). If you plug anything else into it you'd probably void the warranty and damage something.
Oh stop. Nothing happens when you plug a drive in. Literally nothing. Do you actually believe Apple would design a port that is vulnerable to having something plugged into it? They sell these things to families with little kids. If all you had to do was plug a drive in to damage an ATV, the Genius Bar would look like a crowded PTA meeting.
But to get back to the OPs question: No, you can't access media from a drive via that tiny USB port in the back. It's there to connect the AppleTV to iTunes, on a Mac or pc, to restore iOS software in the rare event of a meltdown.