This is a nice idea, (I would say that, because I had thought of it myself a while back). Rather than use Google Docs to convert to HTML, what about using Unoconv to convert to PDF instead?
Alternatively, I have developed the Atto plugin Microsoft Word File Import which contains (mainly XSLT) code to convert .docx files into HTML. You could re-use this code to implement the feature you want, avoiding any external service. (We have found Unoconv quite finicky, and have had to implement a watcher to restart it periodically.)
I think it would also be nice to offer a facility for a Lecturer to opt to insert the content into the File resource Description field, or even permanently replace the File resource containing the Word file with a Page resource containing the converted content.