I'm thinking about starting to write a game and my primary concern is performance. I was thinking about writing it in xna (client), and then also writing the server in c#. Will this be fast enough for any game that requires twitch reactions (like a top down shooter).
Yes. The XNA Framework is perfectly capable of building any type of game. If I were you, I would worry more about building a game first, rather than how well it will run once built.