google-drivesynchronization
Is there a way to download a .PDF or whatever in such a way that it would skip my local machine and be directly uploaded to Google docs?
If that's not possible, is there some solution where I can set up a folder, to download the file to, that will synchronise with Google Docs?
In this viewer you can Edit online or just save it in your Google Docs:
I think they don't have a direct link that you could use to simply convert the files and have them in the edit mode directly. You might have to take the API route.
There's Etherpad, which is a GPL collaboration verion of Google Docs. There are various example implementations which protect the privacy of your documents, although privacy isn't the issue.
Best Answer
You could map a drive to Google docs with the Gladinet "G-Drive". Look here in the Google App market place. Then adjust your browser downloads location to the G-Drive.