We don’t know enough details about how the Horcrux Network and the Special Connection between V and H work, but …

"OBLIVIATE!"

And it all poured out of Harry into the spell.

Harry fell over on his side, dropping his wand, gritted screams coming from his throat, his hands going helplessly to his scar, even as the sudden blast of pain in his head began to fade. Only dimly did his eyes see that the air was filled with glowing snowflakes, drifting motes of silver light like tiny specks of Patronus Charm.

… this is highly unusual for an obliviation, so I think it is very likely that V has not left his body.