I upgraded a 2.1 site to the latest 2.2.4, and the Google Docs repository (enabled and visible) is not showing in the file picker. I thought this may be an upgrade problem, so I tried a fresh 2.2.4 installation. There are no Google Docs in the file picker there either. Google Docs is shown in the file picker using Moodle 2.1 and 2.3 (Oauth2 registered) on the same server. Lastly, demo.moodle.net is running 2.2.3, and Google Docs shows there.
I will report this to the tracker, but I want to confirm it is affecting others.