Can you throw a rock diagonally in curling? It seems it would be beneficial but no one does it?

I'm not sure what you mean. It sounds like a "bank shot" in pool, but curling doesn't have banks. They get the same effect by spinning the stone and sweeping the ice to make it curl. That's why it's called "curling".
www.youtube.com/watch?v=WXHh_wadqPw