Do you think Kagome Higurashi is her own ancestor?
I rather doubt it. That would mean that part of her family has a demonic bloodline, though it'd be rather diluted in the hundreds of years since the feudal era. My brain says that'd be troublesome as a priestess or shrine family.
Oddly enough, though, the demonic blood may not necessarily interfere with her purification powers, as her daughter Moroha seems to have inherited them (based on the trailers). Since she's a quarter demon, it wouldn't be impossible for a descendent another 5 or so generations down, thus even less demon, to have purification too. So it's not impossible she's her own greatest gran. Just. Odd and unlikely imo.
(Though it could be a different power Moroha has, since the eps for Hanyou no Yashahime haven't aired yet. And Kagome passing down her own power, undiluted, that many generations? Ehh..)
I find it more likely that she's descended from a relative of Kikyo. Neither she nor Kaede had kids, as far as we can tell from the original series, but there could be cousins. Given her grandfather cares for the shrine around the Tree and Well, an ancestral connection to Kaede's family is likely. At the very least, someone attached to the village that takes over guardianship of the Tree and Well.
Another option is she's related to Sango and Miroku or Kohaku. There's a passing resemblance between Sota and Kohaku. And their family would have a vested interest in guarding the well. But. Kagome's family is priestly rather than hunters. I also don't much care for the "related to Miroku" theory because uh. Grandpa, NO. Bad flirting. Also makes multishipping hecka squicky if she's their great-etc grandkid.
She's not necessarily related to any of the main characters, though. Quite possibly she's just related to a random villager and oh boy did they luck out not dying in any of the multitude of attacks during the series. Maybe they moved in much later.
Or maybe she's related to that kid the demon crow tried to eat and it's a damn good thing she shattered the Jewel. Kid could've been inspired to follow in her footsteps and apprentice to Kaede...