While I can't give you a definite answer, (hopefully someone will chime it), I've used the circle case since buying the LG G3 in November 2014, and space-wise there is no reason to think that the slight added thickness would prevent the flap from closing, and should not affect the magnet in the flap from activating the screen when the flap is opened.
I have found that the flap itself is a great screen protector and have no scratches on my G3's bare screen. The worse thing that happens is pocket lint finding its way on the screen through the Quick Circle opening. I wouldn't dare put my keys in the same pocket as the phone. I also found it better to put the phone in my pocket up-side-down so that I'm not taking the phone out of my pocket with my fingers on the screen, or pulling on the narrow portion of the flap between the Circle and the top of the flap. HTH