I think either way the answer is still doubtful it will be smooth. Streaming externally (aka twitch) requires both ISP and CPU processing. Local is still CPU processing. So he will still be playing a game and recording. That is muti tasking two heavy hitters for the CPU.
I wouldn't recommend doing either of the two on that setup. Not saying it can't be done, I'm saying it most likely wont be a great experience.