I don't care how old it is, I'm bumping this.
This has a lot of potential, and if someone could code that, it would be dandy. Allow the user to sign in, have the login cache locally.

I've looked into it before; there are no public APIs offered by Netflix which really restricts what can be done to add this feature. This prevents Cinema from being able to grab the video's metadata (title, duration, etc.). There's also the issue of controlling the video playback to synchronize it between players; no public JavaScript player API. Lastly, every time you startup GMod you would need to login again as browser history isn't saved.