Changing from a larger diameter to a small diameter string, will in most applications change your setup. Depending on where you are at on a spine setup with your particular bow, it may throw it off a bit, which would cause a the arrow to act differently, so yes, you might see right to left variations due to a possibly now weak arrow striking the shelf or side plate. If the bow is cut past center it will tend to be more forgiving, so I'd guess the left to right may not be as bad. Up and down may be affected due to it being sped up a bit, giving a flatter trajectory than before, but it will vary.