The illegal votes throw the result of the election in doubt, regardless of whom the illegal voters selected (which cannot be known because of the sanctity of the ballot).
What happens next? McDaniel might contest the results, then due process according to the MS laws regarding elections would proceed. You would need to research MS law to determine what is prescribed.
Though if the votes are concentrated in precincts that go almost entirely for Cochran one can be sure that a solid majority of the votes went for Cochran, and, if there is enough of this, be sure that McDaniel in fact won.