You don't have to, but I highly recommend it. My suggestion is to download the driver you want to your desktop with the old card in. Then, go into "Add/Remove Programs" and completely remove your present ATI display driver and ATI Control Panel (if applicable). From there, if you REALLY want to be thorough (which I recommend), run DriverCleaner so that any old files will be taken care of.
Then, shut down. Swap out your video cards. Reboot. Execute the driver install program you put on your desktop. You'll probably have to reboot after it installs.
In my opinion, that's the safest and "cleanest" way to upgrade a video card. Just did all of that yesterday and didn't have any problems.