Stop action photo's show the thin over-shot wad spinning off to the side well ahead of the shot charge, just a few feet out the muzzle, thus not distrubing it in the slightest. This is probably due to expanding gasses of the charge blwing past the shot charge impacting the wad and separating it from the shot cloud itself.
The heavier the wad, the more likely the opportunity of the wad messing with the shot charge closer to the muzzle before spining off can take place. Stop-action photos also show this happening in un-choked bores, where the shot impacts the wad which presses back on the shot cloud and causes spreading just clear of the muzzle. This is one reason how hollow shot patterns (the dreaded donut of shot patterns) come to exist. I'd assume the distance between the jug choke and the muzzle would be important in this respect, whether the top wads 'thought' there was a choke or not. By this I mean that a short end-choke, would promote normal separation of the wads from the shot charge, while a long end-choke might act similarly to a non-choked gun as far as wad separation is concerned. Again, the heavier the weight out front of the shot shoarge, the more likely the wads will impinge on the pattern. More shot in the cloud tends fill in any shot-cloud damage, but of course increases recoil.
The 'end choke' is the length of cylindrical bore between the choke and the muzzle. In the 'best' modern chokes, this end choke is the same length as the shot column. The most cheaply made chokes are simply swaged constrictions of the muzzle, which then had no end choke. They can be made to shoot exceptionally well through tuning and load development. By tuning, I am referring to opening up the swaged full choke slightly with brake cylinder hones while developing loads. In concert, it's amazing how well you can make a pelter shoot.