Can you upload to iTunes U Google Doc, Sheets and Slides files?

I currently work in a school district that has "Gone Google." Both the staff and students are using Google Mail, Drive, Doc, Sheets and Slides. A 1:1 iPad initiative is starting next fall and we have been asked to look into the use of Google Classroom or iTunes U as a learning management system. I have experimented with both, and while they both have a lot to offer, I would like to use iTunes U. Except there is one problem. The vast majority of the materials I would like to share with students were created using various Google Apps and they are all stored in the Google Drive. Has anyone successfully shared files created in those Google Apps on iTunes U? If so, how did you do it?