I wouldn't think the low frequency drivers would "break-in" very quickly once installed in a damped enclosure.
Mine hardly move at all with normal program material.
Also, the suspensions are just that; they simply suspend the cones and domes and really should not be a significant part of the overall resistive load.
In any event, countering or altering the electromotive forces from the motors would be analogous to a kitten trying to impede the movement of an elephant.
If anything happens to "loosen" the compliance of the suspensions, I would think that those effects would degrade sound quality, not improve it. Similar to a new shock absorber becoming more compliant over time, resulting in reduced damping of vertical shocks to the car suspension.
Any effects that cold storage and shipping has on driver compliance probably constitutes the bulk of the effects of break-in, and should clear up, with or without music being played through the speakers, once the air within the speaker cabinets warms up to the temperature of the listening environment.