No, BUT it can happen. I have 3 full sized mares, a small pony gelding and a mini mare. The mares all love the gelding, and 2 of the 3 will share a stall with him (he and my older TB mare are typically in the same stall.) The herd is well-balanced and while there is a definite pecking order, they all know the routine and their position so it works very well.
That said, when I first bought this farm, the neighbor had previously boarded broodmares here, but they did not use the Dutch doors and the paddock. They stayed here for a few months after we bought the farm and we tried using the Dutch doors, but there were a couple of dangerous situations where the lead mare would boot the other mares out of their stalls, and if they didn’t move quickly enough she would go in with them. Once she kicked another mare and the door, leaving a pretty big hole.
It’s not an ideal setup, for sure. It only works in certain turnout groups. In the past when that was not a safe option, I just kept the doors closed after they were turned out.
I have considered ways to modify the barn setup but there really isn’t any other option, other than not using the barnyard as a dry lot or using stalls as a run-in. Which also has its pros and cons.