I assume this is a dumb question, but if I wanted to try mining for the first time with Grin, running an HP z2 Mini Ubuntu 18.04, could I connect something like this external graphics box and have it work like an integrated card in a desktop? Or would there be a ton more work involved?
You won’t have to buy anything else, but the case is a niche product with a corresponding (high) pricing. In other words, it doesn’t scale beyond a GPU or two. If you don’t want to scale, it shouldn’t be a problem. Go for a quality case with high bandwidth !