The program you execute will run under the root user id and will
generally have no authority to access your X display. KDE su gets
around this by adding an authentication cookie for your display to a
.Xauthority file. After the command
exits, this file is removed.
If you don't use X cookies, you are on your own. KDE su will detect this and will not add a cookie but you will have to make sure that root is allowed to access to your display.