>Can any of the new MBPs run the latest Final Cut Studio 3?
YES. I have it running on a min-2012 MacBook Pro...the latest model of non-retina macbook pro. It runs fine.
>Are the built-in graphics circuits up to handling FCP, or are they limited to just certain models now?
The graphics card doesn't really matter to FCP...it's MOTION and COLOR where it mattered. And it works, but it doesn't boost any performance.