Yes, this should work with the "Logi Options" app. I have been using the new "Logi Options+" app in the beta version for some time now, which works even better for me. Here you can assign the action "Desktop right" or "Desktop left" to the buttons, which switches between the full-screen apps/desktops. You can really set up every conceivable action.

With the software supplied, an almost infinite number of functions can be programmed.