Yeah, you'd have to, but gMail/gDocs is pretty prevalent. I know a bunch of schools already use it for their email/office suite so it wouldn't be too hard to make that requirement. I really like it because it's grabbing metadata out of something people already use rather than having them use some horrible web app from the 90's that was contracted out by a now defunct company.
I am against making anything like this a "requirement." It defeats openness. And all for a stupid anti-cheating system. It's better just to go to turnitin.com
Eventually google docs may become the new horrible web app :)
If I am grading a text for its content, I shouldn't force students to use any particular tool. There should be more evaluation tools that confirm if the student has the skills I'm evaluating for, like written or oral tests in a controlled environment.