I performed this task today on my school's two domains. Teachers are on fatherjudge.com and students are on fatherjudgestudent.com. The process took maybe five minutes to do both domains. I enrolled students from the fatherjudgestudent.com domain into a Test Class I created with my fatherjudge.com account. After joining the class, students were able to create a document in an assignment. The document then appeared in the assignment folder in the class folder in my teacher account's Drive. This is what we have been waiting for to hitch our horse the Google Classroom wagon.
July 14, 2015
Google for Education Adds Whitelist Domain for Google Classroom
This is big for schools that have one domain for teachers and another for students. Now you can whitelist the domains and have teachers invite students to a class even though they are in a different domain. This was the case at my school. When I used classroom this year I needed to have an account in the student domain. This link explains how to set up the whitelist. Make sure you perform the "add domain" to each domain. If you don't whitelist both domains students will not be able to share files from their teacher.