It wouldn't PROVE that they were descended from Jesus, or Mary. Unless they have some way of proving that Mary is the corpse. How would they prove that? Everything is based on some vague riddles, many of which are no longer in existence. It would require a lot of compelling evidence just to prove it was Mary. Tom Hanks saying, "ok but there's this riddle that was in a rubik's cube in this vault that was being guarded by an evil dude who might have worked for this cult that hired people who whip themselves, see..." would not cut it.
They'd have to carbon date it first. Then you could maybe prove the approximate date of the corpse. Then you'd still have to prove that the corpse is mary's corpse, which would require either matching material from nearly exactly the same time, or solid evidence that the corpse was at specific locations at specific times and follow the trail precisely.
So let's say you do that and hundreds of other things and somehow miraculously prove it is Mary's corpse. How do you establish that she had jesus' child? You have a lot of work to do there. Everything is based on assuming that templars did X or that the bible is perfectly accurate. So you have even more work to prove that it would have had to be jesus' baby.
Of course, her having a baby in and of itself would be fairly exciting.