I'd like to see OTR implement some of the groupchat enhancements of this, or at least see a TextSecure implementation for the desktop.
Right now the protocol includes multi-device support, so the foundation is there for developing desktop and tablet apps that work seamlessly in conjunction with your phone. Our first desktop implementation is likely going to be a browser extension, feel free to jump in and get involved with that if you'd like.
Are the messages only delivered to the 'logged in' clients? So if I am logged in on the desktop my message exchanges are also sent to the phone client? But any messages I send/receive from my phone while logged out of my desktop are synced through the server on login?