No it's not a reason why aircrafts do turn when banked.
But yes, discrepancy between center of lift and center of mass produces a torque.
Ideally, center of lift= center of mass. If this is not the case you need to trim your controll surfaces to account for the torque (unless it becomes too extreme in which case the aircraft becomes uncontrollable/unstable)
That's why rules/guidelines exist for all (military and commercial) aircraft how much mass imbalance you are allowed to have, in which order you are allowed to fire your weapon, and in which order you have to deplete your different fuel tank cells and so on.
As we dont have trim in A3 it should be avoided to have center of lift outside center of mass/ vice versa.