If the burrs are blunt (which Im certain yours would be after that sort of work), the burrs will be tearing and rubbing the beans rather than slicing them. This will lead to less consistent particle size which can lead to earlier blonding and less shot to shot consistency. Just as cutting with a sharp knife is quicker and requires less effort than a blunt one, grinding with new burrs will be faster and generate less heat which apparently makes a difference to the taste (one reason why the big grinders have a slower rotation speed).
So long as you keep things clean and follow any provided instructions I doubt youll have any alignment issues. If you have muck between the burrs and the mounting planes youll obviously get them offline but if you keep it all clean you should be OK (have never replaced burrs yet so cant honestly say).