So the question is, if I use the GPU for my video output to the monitor, is that going to screw with it's ability to mine? Do I need to get some cheap cheezy GPU for the connection to the monitor, or will the video really not matter much since it'll just be the monitoring page for the mining software?
It won't matter much if at all. With intel systems I usually utilize onboard graphics for this purpose. In some rigs it helps a little bit (sometimes one card shows a little lower hashrate than the others), and in some rigs it doesn't make any difference at all. You won't have any onboard graphics with your ryzen system, and I don't think it's worth it to bother adding an extra gpu just for display purposes.