You can now signup to test/preview Google Classroom.https://classroom.google.com/signup
If you have a Google Apps for Domains (Education) you should be signed in with that account before you go to the page.
I'm still waiting for my approval, but so far the feedback is that the offering is rather simple. But that's good! LMS are far too complicated today and disruptive innovation usually happens at the bottom end of the market. Perhaps the LMS does not need to be all things to all people. Perhaps we've been asking developers to make another behemoth like Microsoft Office/Exchange when we really needed Google Apps.
As always, we shall see.