The answer is yes, the stator and rotor will try to align themselves. In most cases, this is only a problem with sleeve (babbitt) bearings or roller bearings.
In the case of the babbitt bearing, there is usually up to 1/2" of endplay allowed and, if during alignment, the shaft is not located on magnetic center then damage will result. If the shaft is pulled to the inner or outer extreme of the endplay, the shaft journal will ride against the inner or outer thrust face and, because there is no 'mechanism' for delivering oil to the thrust face, bearing failure will result.
In the case of the roller bearing, it is more difficult to 'accomplish' this type of misalignment because there is very little endplay in the bearing. However, if you are 'forceful' in the alignment you can end up with axial thrust load on the bearing. In this case, the ends of the rollers will ride against both the inner and outer bearing races on alternate sides and this will result in quick bearing failure.
Ball bearings are more forgiving. I imagine that in the extreme case that it would be possible to cause a bearing failure due to axial misalignment but this, being the extreme case, is not common.