I do not believe that someone could actually trace their family bloodline back 2,000 years. But the fact is, even if they did, being distantly related to someone related to Mary or Joseph might be an interesting topic of conversation, but it wouldn’t mean anything else.
I have a sister-in-law who can trace her ancestry back 1,000 years. She is Finnish, and virtually every Finn can do the same.
Ever since Christianity came to Finland about 1,000 years ago, the Church there has kept meticulous records of every birth, death, marriage and baptism, and those records have been preserved to this day.
Perhaps the Syriac Orthodox Church has similar records, either written or oral. Personally, I would be curious to find out. But, of course, I don't fault anyone else for being uninterested.
I happen to be fascinated by genealogy, in general.