One of the last, big missing features in LibreOffice is collaborative editing, to fill this hole Eike Rathke (of RedHat) has been working for some weeks getting Telepathy code hooked into the LibreOffice core. This was chosen to allow us to setup a channel for multi-way communication over existing Instant Messaging (IM) protocols, without requiring any form of server.
I've got a private (non-collaborative, but potentially collaborative) OpenOffice cloud setup. You use VNC on localhost, pick it up and redirect with Guacamole (still on localhost) and redirect to *443 with Apache.
Well, I thought of it myself, yes. I actually use eyeOS for my cloud server - but only as a drag&drop file managing surface (I don't use the eyeOS apps, but have installed my own). If you add webdav, you have the same docs with native applications at home, with apps on your mobile and with OpenOffice on any borrowed PC.