He could very well be inside Harry or Nothing - at least not as a direct result of the possession
The answer really depends on how you interpret the quotes and for that reason I am going to give a discussion for both sides.
The first example I'm going to look at is the Pensieve!
Harry was thrown forward and pitched headfirst into the substance inside the basin –
But his head did not hit the stone bottom. He was falling through something icycold and black; it was like being sucked into a dark whirlpool –
Goblet of Fire - Scholastic Ebook - Page 373
Another excerpt from OOTP:
He took a great gulp of breath, and plunged his face into the surface of Snape’s thoughts.
once, the floor of the office lurched, tipping Harry head-first into the Pensieve…
He was falling through cold blackness, spinning furiously as he went, and then -
Order of the Phoenix - Scholastic Ebook - Page 482
There is also an answer here on the same topic.
In this answer @Richard also talks about the language used to describe his return from the Pensieve and the fact that Snape has to go into the memory to retrieve Harry from it instead of just raising his head out of the Pensieve.
However one can also ask the question "If his body is in there how would Snape know he was in there?" we can also argue that the language used is merely a feeling that is Happening to Harry rather than the actual action. (Like the feeling of falling when going to sleep)
When Harry talks to Toms diary in CoS the diary says "I can show you" the following quote then seems to describe Harry being absorbed into the book similarly to the Pensieve.
Harry saw that the little square for June thirteenth seemed to have turned into a miniscule television screen. His hands trembling slightly, he raised the book to press his eye against the little window, and before he knew what was happening, he was tilting forward; the window was widening, he felt his body leave his bed, and he was pitched headfirst through the opening in the page, into a whirl of color and shadow.
Chamber of Secrets - Scholastic Ebook - Page 158
Following this we have a description of Harry coming out of the diary:
Harry felt himself falling and, with a crash, he landed spread-eagled on his four-poster in the Gryffindor dormitory, Riddle’s diary lying open on his stomach.
Before he had had time to regain his breath, the dormitory door opened and Ron came in.
“There you are,” he said
The language used definitely implies he fell from somewhere or was ejected from somewhere with some sort of force at least. We also have the comment from Ron which seems to imply that Ron was looking for him, it seems obvious that he would have checked the dorm room before and Harry was clearly not present.
Other than the language points mentioned before there's not really much of an argument against this point apart from it's possible Ron had just gotten into the Dorm when Harry stops peering into the book.
There is only one description of Legilimency that we have available:
A hundred Dementors were swooping towards Harry across the lake in the grounds… he
screwed up his face in concentration… they were coming closer… he could see the dark holes
beneath their hoods… yet he could also see Snape standing in front of him, his eyes fixed on
Harry’s face, muttering under his breath… and somehow, Snape was growing clearer, and the
Dementors were growing fainter…
Harry raised his own wand.
Snape staggered - his wand flew upwards, away from Harry - and suddenly Harry’s mind was
teeming with memories that were not his: a hook-nosed man was shouting at a cowering woman,
while a small dark-haired boy cried in a corner… a greasy-haired teenager sat alone in a dark
bedroom, pointing his wand at the ceiling, shooting down flies… a girl was laughing as a
scrawny boy tried to mount a bucking broomstick -
Order of the Phoenix - Scholastic Ebook - Page 446
The above does not feature any of the language present in the former quotes to suggest an absorption of ones body into the memory. This is also probably the most related piece of magic to what is being used between Voldemort and Harry, although it could be argued because of the Scar being
not a Horcrux the magic is most related to the Diary.
For the reasons listed above I believe that it is largely based on your Interpretation of the language being used as to where you think Voldemort goes.
Discussing the actual scene
We all know that after Voldemort is finished with Harry he reappears and then takes Bellatrix and leaves. In the scene he is actually forcibly ejected by Harrys or by his strong feelings of love which cause Voldemort pain.
To me it makes little sense for Voldemort to return from wherever he was to simple collect Bellatrix and then leave again. It would make more sense if he was ejected from Harry and then returned to the room from his mind, forced to retreat he collects his Lieutenant and leaves. Some may argue that he cares for Bellatrix and returned for that reason which is entirely plausible
It is also plausible that he returned not to run away again but to finish off Dumbledore and Harry, until the MoM shows up and ruins his plans he then makes the tactical decision to retreat.
For a few seconds Voldemort was visible only as a dark, rippling, faceless figure, shimmering
and indistinct upon the plinth, clearly struggling to throw off the suffocating mass.
Then he was gone and the water fell with a crash back into its pool, slopping wildly over the
sides, drenching the polished floor.
From this it definitely sounds like Voldemort disapparates when he is encased within the water.
And then Harry's scar burst open and he knew he was dead: it was pain beyond imagining, pain past endurance.
He was gone from the hall, he was locked in the coils of a creature with red eyes, so tightly
bound that Harry did not know where his body ended and the creature’s began: they were fused
together, bound by pain, and there was no escape
And when the creature spoke, it used Harry’s mouth, so that in his agony he felt his jaw move
Nothing in the book seems to suggest Voldemort reappearing, but what it does suggest is him entering Harry, at least more so than any previous encounter Harry has had with Voldemort.
Based on the time difference between the two quotes or more aptly between when Voldemort disappears and then Harry feels the pain, it's safe to say that Voldemort went somewhere before possessing Harry. What is uncertain is whether or not he entered Harry after this fact.
Whilst the Pensieve and Diary arguments are very convincing and definitely seem to side more with someone entering a memory, I think that Legilimency is the closest representation of the Magic that is the connection between Harry and Voldemort. The quote we have for Legilimency definitely makes no mention of physically entering the memory or even of a feeling of leaving his feet or landing after the fact. I think that both Bellatrix and the opportunity to kill Dumbledore and Harry would make more than a compelling argument for Voldemort to return from wherever he went. Also the time difference between his disappearance and Harry's possession seals it for me, If he was being absorbed into Harry why not do it straight out of the water tomb.
TL:DR I think he Disapparated but you may think differently