Is the mid bead some assist if the butt stock doesn't fit properly?
Yes, and no. It's a two-edged sword. A mid-bead can be of some assistance to a shooter, whose gun doesn't fit exactly, by allowing him to get used to how he must adjust himself to get the gun to shoot to POA. However, it can also be a detriment in that, if the mid bead (or the front bead for that matter) causes him to look at it as he swings on the bird or target, he will certainly miss, and he will miss behind.
So again, it may be useful to a pre-mount shooter, or someone getting used to a new gun, but is useless for snap shooting, or low gun.
I will not go so far as to say that the front bead is useless, too. We are never to look AT the bead/barrel/muzzle during the shot process, but IMHO the front bead is a reference point that is in your field of vision and gives a bit more reference to the subconscious as to where the muzzle is. My reasoning for this belief is this: I have been amazed, for many years at sporting clays, at how much precision is necessary to kill a going away target with a shotgun. One would think that, with the pattern spread that a properly choked shotgun has at 25 yards, it would be good enough to just cover the bird with the muzzle(s). But, I have found that is not the case at all. I have missed targets where the trap is directly in front of, and below me, with my muzzle covering the bird, but not precisely centered, many times. So many in fact, that I now make myself take the shot slowly and make sure that front bead is directly on, or in line with, the target. I never look AT the bead, or barrel. My focus is hard on the target. But it pays me big dividends to take a second longer to be sure it's centered, whether bird or clay. There are those few individuals that can shoot from the hip nearly as well as the average shotgunner can from the shoulder. Obviously, the bead is useless to them, doing that. But, most of us mortals are not that person. I need all the help I can get!
Lastly, a nice double gun with the front bead missing is like a beautiful woman that smiles at you and you realize she's missing a front tooth. She can still function without it, but she's not all that she could be. It is not my intent to demean anyone but, if a shooter cannot shoot well without removing the front bead he/she needs some coaching in how to focus their vision on the target.