Tried that today and come to find out that files cannot be uploaded to Google Docs through the laptop computers we were using, and they'll only send through Gmail if we're using the older version. So what I've resigned myself to doing is creating a conversation between the class email I set up and myself. They'll download their most recent file from the conversation and email it to me when they're done at the end of the class period.
In the end, teachable moment was about problem solving. An added bonus: most of my students don't have email addresses, so they'll learn how to attach a file before the get to the high school.