No. That's little more than Dark Brotherhood fantasy - any group which delusionally venerates Sithis as a 'god' probably shouldn't be listened to when they ascribe other aspects to it. Would you call the Force in Star Wars a 'god'? That's roughly Anuiel and Sithis's metaphysical equivalent. Oblivion turned him into the Grim Reaper because Oblivion's Dark Brotherhood was written by people who needed an expedient Grim Reaper anologue, not out of faithfulness to his depiction in the Elder Scrolls' religious literature.
And "the Dark Brotherhood says so, and they don't know what they're talking about, so it's not true" isn't even my best case against this. Just think for a second what you're saying, in geographical terms, as geography is really the only way to make sense of this. "The Void" is commonly understood to be the expanse of nothingness surrounding Anu, Padomay, and the Aurbis, which is itself a flat circle at the intersection between Anu and Padomay. The Void is nothing. Auriel and Sithis, on the other hand, are aspects of Anu and Padomay that were inserted into the Aurbis upon its creation - they themselves are not sapient, not "people", so to fulfill this role they had to birth avatars of themselves, their "souls" known as Auri-El and Lorkhan, to populate the world of Spirits.
http://i.imgur.com/JiYW4vm.png if it makes my point clearer.
What this means is that Sithis does NOT come from the "Void" - he comes from Padomay, which is one half of the extant universe. "Coming from the Void" is, incidentally, an oxymoron.
Except the Nine aren't in Aetherius. They are in Mundus. Magnus and the Magna-Ge are in Aetherius (Auriel also made it back at a later point.) This was the whole point of Creation, and also, as I explained before, why the Eight Dominion Planets hang in the sky along with Nirn. All are Mundrial. Thus it follows that mortal death doesn't lead to Aetherius, because how could it? An important quote, courtesy of our friend, the ever-helpful http://www.imperial-library.info/content/loveletter-fifth-era-true-purpose-tamriel
So dead dudes go to either the Dominion Planets of the Aedra or to the Oblivion Realms of the Daedra. Sovngarde isn't actually in Aetherius, it's on the cloven divinity of Lorkhan, either the moon Masser or the moon Secunda, where it logically follows that it should be. If Lorkhan hadn't had his body ripped in two, he'd also be a Dominion Planet. If you want to argue against that, then feel free to explain one, why the god who sacrificed everything to create the Mundus would leave it, and two, how he was able to leave it given that he is extra-double-dead. "But my Skryim character wrote it in his journal entry!" is not sufficient evidence to overturn the workings of the Aurbis. This is also a teachable moment for why Bethesda's writing is neither fully self-consistent nor infallible. In such situations, the greater evidence wins out over the weaker evidence, as it does with the matter of Sithis's "divinity."
People like to think of the extra-Mundrial realms in terms of Christianity, with Oblivion as Hell and Aetherius as Heaven, which is natural given our culture, but unfounded. Aetherius is most definitively not Heaven because the gods don't live there and (virtuous and faithful) dead people don't go there. If either of these things were untrue, then the entire point of Creation would be invalidated.
Oh, and to answer your original question:
Sithis. Easily.