Not really.Putting the bead where you want it will absolutely work if the second required point is where it's supposed to be.
It is pretty common for shotguns not to hit where the bead and correct head position are aiming. It can sometimes require bending the barrel/stock to correct left-right POI issues or adding shims to correct elevation issues.
You can't count on a shotgun with a true POI without doing some work on a patterning board to check it out. Not doing so has saved a bunch of turkeys and even ducks/doves, etc.
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