Would it work to hook up a webcam (which already has a live image if you hook it up to the usb port on your computer)
No: the PC is doing a lot of work, by Arduino standards, to generate that live image from the webcam data.
It's like hooking an RV to your bicycle: you might be able to generate a little movement movement with a lot of effort, but it's not a feasible way to do any real travel.