When deployed, SproutCore is only static HTML, CSS & JS files. This means you can serve them from any server: Apache, nginx, IIS or any server that can serve up plain old text files.
Ruby is only used in development mode, it has a server, which keeps track of files that you've changed (to make reloading faster), and a build script which takes the many files (split to make debugging easer) and joins/minifies them. Once built, you can take these files and put them anywhere, no ruby needed.
On your server side, you can use what ever tech you want for authentication/ data persistance. In your case you would use ASP.NET, to write your API that would send and receive JSON (or XML if your so inclined).
See http://wiki.sproutcore.com/w/page/12413020/Todos%2006-Building%20the%20Backend for examples on how you would write your server.