Harry is not a real one no spell was cast .And he is not a dark object. You need to cast the spell. Making it Nagini. Harry only holds a soul fragment.
In the book, the Horcrux is identified as an object CONTAINING a soul fragment, which meant Harry WAS the seventh Horcrux.
Near the end of the last book, Harry is blasted by a second Killing Spell and survives yet again, but the soul fragment within Harry is destroyed.