The shoulders or shoulder muscles (and bicep muscles) are lifters so they cannot exert force into the swing.
By lifting the arms though to a degree that stretches the arm muscles and core muscles, the shoulders are essential in the load position.
Once the arms are below shoulder level the shoulders do act more as a linkage and aid in controling the bat along with back muscles, but in my view this is subconscious movement.
The shoulder tilt that helps deliver the bat to the ball at the proper angle is more a result of the myriad core muscles again subconsciously if the eyes are on the point of contact.
(I often remind batters that there should be no bicep tension in the swing.)
.