hmm well it used to be that you curl the file down, which could have been tied into a cron job, but seems they turned that option off.
A quick look at the docs hints you can fairly easily use the api to export and download the Excel file. I have never done this, but if its anything like using the calendar API, you will probably need to add a library to your project and set an Oauth token.
You could try googling around, i bet someone out there has written a perl/python/bash script to grab a file from google drive. If the file is publicly accessable, I can’t see why you cant just curl it, but i’ve seen reports of google restricting it.
A cheeky way might be to something similar to the dropbox sync, but rather install the google drive app on your sever if your able to (you would need a VPS for this). You could then symlink the file into your content folder.