Probably yes. You can't really know until you try.
Indeed AMD is notorious for having driver problems, especially on the Windows Vista 64 bit platform.
Id recommend googling what AMD drivers fix this issue, and if none can be found, getting a different card or upgrading to Windows 7.
Like Sunius said, try a different driver version.
Did you completely uninstall any old drivers and card before you installed the HD7750? I'm using the 12.4 drivers with my new XFX HD7750, and having no problems; in fact [driver] issues I was having with a GTX560Ti seem to have gone away.