The screen saver does not interfere with the changing of screens or anything else. It simply "inverts" the colors on the screen. The "inverse" of a color (in this context) is its RGB complement. Its RGB values are inverted. Not sure how else to explain it.
Nevertheless, it works on everything on the screen. Including cell borders, images, everything.
To get an idea of what it does, just go to the Preferences tab, check "Enable Screen Saver", set "How often" to 5 and "For how long" to 3. Now go to the Tournament page and watch.
Of course, you don't want values that small during your live tournament.