No, it will have an equal but opposite effect. Think of the arrow as being on a pivot point above the grip in it's standard location. If you move the rest 3" back and pivot the bow backwards, the arrow point will drop. If you mount the rest 3" forward and pivot the bow the same way, the arrow will raise. That is why your form has to be exact when shooting an overdraw bow.
Brace height really has nothing to do with it. A long brace height has the effect of making the bow more stable regardless of rest position, up to a point. This comes from the grip sitting even with or in front of the limbs.