This new Chrome extension is great news for our team. We co-author heavily in Google Docs. We too had trouble connecting with Jetpack on one site, and it seems when you change over from HTTP to HTTPShttps, some of the Jetpack features, among them the Google Doc Extension doesn't work, without disconnecting on both sides. After disconnecting the site from my WordPress.com account and disconnecting the Jetpack instance on the site, and then reconnecting, would allow a proper authentication of the Google Docs.