It is possible but complex because you would almost certainly need to replace the ubuntu kernel with the one used on the Linaro RPB images.
The best starting point would be to install the RPB debian release to both eMMC and SD card. You can then use the SD card debian installation to run debootstrap (pointed to the ubuntu servers) to populate an /ubuntu directory on the eMMC. Finally you would be need to merge the file systems to preserve the /lib/modules and /boot directories from the debian build.
That will give you Ubuntu but, even then, its not ideal for Unity since the 3D graphics probably won't work (and wouldn't support full OpenGL if it did).