There is a very good chance that your card will not work properly with Windows 7. So you have to prepare yourself for that unwelcome news.
But yes, you should try installing the driver
any way you can before giving up.
Keep in mind that the catalyst software package contains more modules than just the card driver. Some of the features of the old Catalyst software may not run in Windows 7. So if you try compatibility mode and it does not work to install the entire package, then the next thing to try would be to run the package in compatibility mode, select a Custom install, and try installing the graphics driver only.
If none of that works then you are left with only two unfortunate choices: Buy a compatible video card, or go back to XP. There is no magic fix to incompatible hardware.