harry potter - What would be the effects of the Dementors' Kiss on a Horcrux contained within a living person?

Could the Dementors’ Kiss destroy a living Horcrux, like Harry? Lupin explains the Dementors’ Kiss to Harry in Prisoner of Azkaban:

‘They call it the Dementors’ Kiss,’ said Lupin, with a slightly twisted smile. ‘It’s what Dementors do to those they wish to destroy utterly. I suppose there must be some kind of mouth under there, because they clamp their jaws upon the mouth of the victim and – and suck out his soul.’

Harry accidentally spat out a bit of Butterbeer. ‘What – they kill –?’

‘Oh, no,’ said Lupin. ‘Much worse than that. You can exist without your soul, you know, as long as your brain and heart are still working. But you’ll have no sense of self any more, no memory, no ... anything. There’s no chance at all of recovery. You’ll just – exist. As an empty shell. And your soul is gone for ever ... lost.’

Prisoner of Azkaban - Page 183 - British Hardcover

Subsequently, Dumbledore tells Snape in The Prince's Tale in Deathly Hallows:

'On the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself on to the only living soul left in that collapsing building.

Deathly Hallows - Page 550 - British Hardcover

I noticed that it says the portion of Voldemort's soul latched onto Harry's soul, but it does not specify in canon that the two souls assimilate one another, as opposed to co-existing (aside from Dumbledore saying, 'To speak of one [Harry] is to speak of the other [Voldemort].')

When delivering the Kiss would a Dementor be able to tell there was a portion of another person’s soul along with the victim’s own soul? If not -- based on what we know about the Dementors’ Kiss, Horcruxes, and the soul from canon -- could the Dementor destroy the Horcrux portion of the soul while leaving the victim’s original and untainted soul untouched and intact? Or would both portions of both souls be sucked out by the Dementor?

From the King's Cross chapter in Deathly Hallows we know it is possible for the Horcrux portion of attached souls to be destroyed while the other part lives. Based on what we know from canon could the Dementors' Kiss be a means of destroying a Horcrux?

Related question HERE. (What effect would the Dementors' Kiss have on Voldemort prior to the destruction of his Horcruxes?)

Answer

I'm going to go with yes.

First, evidence that the soul would be (effectively) destroyed comes from Lupin's quote:

your soul is gone for ever ... lost

Now, the question is whether the dementors could suck the foreign soul out:

they clamp their jaws upon the mouth of the victim and – and suck out his soul

Now, I'm going to go (a bit) out on a limb and say the Harry in the King's Cross Station chapter was really just his soul. The fragment of Voldemort's soul was there just as Harry was. So I'd say that the two souls inhabit the body in the same manner and so can be removed in the same manner. We know a dementor can suck out the primary soul within a body, so I think from this we can infer that a dementor could in fact extract the fragment of Voldemort's soul from Harry, destroying the horcrux.