I successfully installed the atidrivers on a live usb system.
First of all you need an empty stick - i used one with 16gb of space.
Put the live-cd in and install a system as u normally would install on an external hard drive.
Its neccessary that you use the instructions of method 1.
Then you already have a system with login on your usb stick.
Next you download the driver from AMD
Install the the driver the ubuntu way.
Its all tested with Ubuntu 12.04 amd64 version. If your getting problems let me know.
Because I am a new user I can't post more then 2 hyperlinks so I definitly would posted the complete solution.
But I will do a post on my blog the next days.