Before Ubuntu Touch Apps can work nicely from the desktop, there's issues to work through with touch versus keyboard/mouse input, toolbar interaction, menu/UD integration issues, scrollbars, full-screen modes, packaging of Debian and Click packages co-existing, tabs, and other features. Usability testing also needs to happen to see just how well the mobile-focused apps will work on a desktop version of Ubuntu.
Among the Ubuntu Touch apps that are being sought after right now for bringing to the Ubuntu desktop include its applications for camera, photo gallery, media player, web browser, notes, and OSK. This is rather surprising given that many of these original Ubuntu Touch Apps are far from being baked and lack many critical features found in other platform's phone apps or the features offered by the equivalent programs currently on the Linux desktop.
The priority items that the associated Canonical developers will work on during the Ubuntu 14.04 cycle to achieve this goal is support for the toolbar, tabs, windowed vs. full-screen differences, keyboard navigation, and scrollbars support.
More details on the Ubuntu Touch Apps on the Ubuntu desktop plan can be found from the video below or the session notes.