I would also love to hear any success stories here. I converted my wife's Macbook over to Linux Mint somewhat recently and the best I could do was setup a shortcut to the Web version of her iCloud.
Google Drive also does not have a Linux client, which is a little surprising. It looks like maybe Box.com supports WebDAV and Dropbox has a first-party Linux client. I haven't tried either and I haven't found anything else yet.