I really do not know what all this speculation is about. Our present monarch is not the rightful holder of this title if you believe what Tony Robinson found out when he was researching the royal tree. In the dim and distant past some king or other, can't remember the chap's name, supposedly sired an heir when he had been out of the country for over 10 months, and wifey had remained in England. TR traced the lineage down from an undisputed heir and the rightful monarch is a chappie who lives in Australia!
So to answer the question re Harry......doesn't seem to matter who supplied the little swimmers.....it seems to be sorted out by onto which sheets you are born!