I don't even want to think about this. If you mean that the stylus cantilever is not parallel to the sides of the cartridge body, how do you align the cartridge? Did you install at a slight angle so that the cantilever, but not the body of the cartridge, is parallel to the little lines on whatever protractor you use?
To the extent that the offcenteredness affects the alignment of the stylus relative to the record you are playing, yes it will affect sonics, and maybe damage your records.
To the extent that the offcenteredness affects the alignment of the stylus relative to the record you are playing, yes it will affect sonics, and maybe damage your records.