I don't see how. Sure, if you had mitochondrial DNA from your long-dead male ancestors, you could suss out your true patrilineal line of descent, but it's extremely unlikely that such data is available. You might be able to get it by inference by analyzing the fanned-out descendents of a relatively recent putative paternal ancestor - back 8 or maybe ten generations, but even that's unusual. And, if you're targeting a specific ancestor, it requires an unbroken line of paternal descent - as soon as your path to, say, Henry VIII goes through a female descendent, at any generation, you've lost the Y chromosome relationship. Same argument applies with the sex roles reversed for females and mitchondrial inheritance. At ten generations back, you've got 1024 grandmother leaves on your tree. Only one of them is your mother's mother's .. mother's mother. At 20 generations (say, 500 years, so the actual age of Henry VIII), you've got a million grandmother or grandfather leaves on your tree, and only one is purely matrilineal, and one purely patrilineal. (That doesn't mean, of course, that you've got a million distinct grand^20 fathers - it'll be way less than that, because the some men will appear on many different leaves, and the same for mothers. But the odds that the path you claim to Henry VII is purely maternal or purely paternal are still very small.

Sure, but unbroken patrilineal or matrilineal lines of descent are rather improbable over such long times - any family that had only sons or only daughters breaks the line, and that's not particularly uncommon. Add some infidelity into the mix and it becomes even harder to believe.