Pursuant to THIS QUESTION (Could the Dementors' Kiss Destroy a Living Horcrux?), I have a follow-up question. Based on what we know about the Demetors' Kiss, the soul, and Horcruxes from canon, what effect would the Dementors’ Kiss have upon Voldemort prior to all his Horcruxes being destroyed? If Voldemort had received the Dementors’ Kiss and had his soul sucked out, would his Horcruxes keep his mind intact? Or would he be turned into a shell of a person, like anyone else who received the Kiss, existing forever in a vegetative state, kept physically alive by his Horcruxes? Would natural death ever occur?
I'm going to make 2 assumptions here, which AFAIK are NOT either supported nor refuted in the canon.
Dementor would be willing and able to suck out 1/7th of a soul (likely true but no canon info).
Not supported/refuted anywhere in canon but makes sense, a soul is food for them so 1/7 of a portion is still worth going for.
AND that the 1/7th of a soul would NOT be prevented from being sucked out by the existence of Horcruxes.
Not supported directly in the canon, but such separation is possible via other means (Avada Kedavra) so no reason why Dementor wouldn't be able to do so.
Assuming that both are correct, which is likely (and if they are not, the answer is trivial - "Nothing would happen from Dementor Kiss at all"), we can make our logic based on the following facts from canon (no quotes yet):
We know that what Dementor does is separate the soul from the body to suck it in.
We know that Horcruxes do NOT prevent the 1/7th of Voldemort's soul from being separated from the body
We know that Horcruxes DO prevent the the 1/7th of Voldemort's soul from "dying"/"passing onto another world" which the separation from the body would ordinarily do
We know that Dementor's kiss doesn't actually kill the body, merely makes it an empty vessel.
As such, we can reach the following conclusion:
Voldemort's body would not be destroyed, but NOT due to Horcruxes. It will die a natural death eventually, like any other victim of Dementor's kiss
Voldemort's soul chunk WILL be separated from the body.
One completely unknown thing is whether the sucked out 1/7th of a soul would be devoured/destroyed by a Dementor, or whether the same forces which keep it in this world and able to exist outside a body would ALSO prevent it from being eaten by the Dementors.
If the former, then the body would exist as a shell and eventually die, just like any other Dementor kiss victim
If the latter, then the "burped out" chunk of soul would be able to return back to the body and rejoin it, since it was able to do so with pretty much ANY body (Quirrell, new body from GoF etc...).
I agree with DVK, however, I believe that after the soul is sucked out of the body, he will not be able to die of natural causes. We know that Voldemort lived for many years not being part of any body, so the fact that the one he was in is now an empty vessel does not mean he is still attached. It was his soul that filled the vessel, not a part of his mind. Therefore, he would still be alive, but it would be up to the other horcruxes to detatch themselves from their object (i.e. locket, necklace, cup, etc.) in order for Voldemort to take a human form once again. Tom Riddles diary prior to destruction would have been the entity to be able to succeed in such an endeavor.
I'm going to mention this, just because nobody else has. When Voldemort attacked Harry for the first time and his Avada Kedavra backfired, his 1/7 of a soul went into Harry, his body was destroyed but his Horcruxes kept him in a semi-alive state, able to possess people and animals. This is what would probably happen if he was kissed; his 1/7 of a soul would die, his body enter vegetable/soulless state, but he would still be able to move around and possess entities because of his Horcruxes, in a similar manner to the time after his backfiring curse.
Voldemort WOULD become an empty vessel as he has already locked 6 sevenths of his soul in horcrux's so what's left in Voldemort himself IS actually his only soul. If a dementor sucked this out then he would have no soul left in his actual body at the time. But what we don't know is if when this happens would one of the horcrux's you made sense this (so to speak) and release part of your soul back to you to keep you a functioning person? Maybe not as all we are told when making a horcrux is "you cannot die" but losing a soul is not dying as we all know so I think the horcrux would be a moot object in this scenario.