You could pull something like that off using cloud-to-cloud-sync or desktop-to-cloud-sync services.
An example for Cloud-to-cloud is CloudHQ. It starts from $ 4.90 a month..
If you want a syncing app that makes your Google document available for editing locally, you should take a look at InSync. Use SugarSync to sync the Google Drive folder (which is in your InSync folder) your document is in. I frankly don't see the point of doing that, but it is a solution. InSync is currently free because it is in Beta.
Installing Google Drive is not a solution because the Google Docs are not saved locally for editing but are represented as a link to your online account. This is the same reason why you cannot use GoodSync: It would only sync a URL shortcut.