I'll start out by saying "I don't know", so I guess I should not be answering!
From my experience using both open and tube type red-dot's there seems to be very little if any parallax even at close distances. I use them on two shotguns for turkey hunting and an AR and sometimes mount one up on a pistol.
I have tried the "put the dot on the target and move my head around" trick with all of them at various ranges, mostly close though, 20 to 60 yards. I see very little if any movement of the "dot" off the bull even when I move my head to the point the dot is at the edge of the lense.
Certainly not scientific, but that has been my experience. My uses for red dots has always close range and with firearms that I am not concerned with pin point accuracy.