Have you tried it? I just installed gamescope and launched some games with it via steam launch options. So far I feel like the frame times are better. I use it on top of KDE and with an AMD card. Freesync in Gamescope works too. (Have it allways on in KDE if that matters).
Whats wrong with saints row 3 and 4 ?
When I would use the mouse the framerate would dip down to about 20. Gamescope was a real life saver on that one because I was out of the refund period when I was finally able to play them.