Another problem with this approach... Jesus is blood relative to Mary and "adoptive" son to Joseph. Joseph was the blood relative to David. Jesus came from the family and lineage of David but, through the work of the Holy Spirit, He was born of a virgin.Mary didn't just pop up out of nowhere, she was also of the House of David. It was tradition that she would marry within her tribe, Judah, which was part of the House of David. There's bound to be decedants of Judah that could be tested.
I haven't looked at the Bible in a while. Where does it specifically say anything about Mary's ancestry? Besides the assumption about the Judah tribe.