Heights aren't going to cause anything to be off center. Given that the work is happening from a fixed point IE the work coordinate then all the math is done from that point. If something is not located where it should be when the code is run that is indicative of either a mechanical problem or a geometry problem. I'm just trying to piece together what you are actually trying to describe.
If you make an error in height settings you'll either have a problem of cutting too deeply, not cutting at all or crashing into the part. Off center doesn't really come into play.