Strictly speaking "overwinding" just involves adding more magnet wire to pickup the induced signal and shouldn't affect the static magnetic field so the distance can remain the same. But some "overwound " pickups also replace the magnets with stronger ones, or ones with a more directily oriented field and these create the issues you're worrying about. Perhaps is you were to describe the particular model PU you're interested in someone here will be familiar with them and give you a better answer.
Overwinding a pickup is just winding more wire to the coil. It gives more output but less high frequencies. It has nothing to do with the magnet. The string to pickup distance is only a matter of taste (tone taste), as long as the magnet is not so close that it chokes the string.