Não, um horcrux não pode ser feito acidentalmente, e Harry não era um horcrux
“By an act of evil — the supreme act of evil. By commiting murder. Killing rips the soul apart. The wizard intent upon creating a Horcrux would use the damage to his advantage: He would encase the torn portion —” “Encase? But how —?” “There is a spell, do not ask me, I don’t know!” said Slughorn shaking his head like an old elephant bothered by mosquitoes. “Do I look as though I have tried it — do I look like a killer?”
-Harry Potter and the Half-blood Prince
Voldemort claramente não matou Harry com sucesso. Ele poderia ter pretendido fazer uma horcrux, mas ele não teve sucesso. JKR confirmou que Harry não era um horcrux.
"Here is the thing: for convenience, I had Dumbledore say to Harry, "You were the Horcrux he never meant to make," but I think, by definition, a Horcrux has to be made intentionally. So because Voldemort never went through the grotesque process that I imagine creates a Horcrux with Harry, (SU: Mm-hm.) it was just that he had destabilized his soul so much that it split when he was hit by the backfiring curse. And so this part of it flies off, and attaches to the only living thing in the room. A part of it flees in the very-close-to-death limbo state that Voldemort then goes on and exists in. I suppose it's very close to being a Horcrux, but Harry did not become an evil object. He didn't have curses upon him that the other Horcruxes had. He himself was not contaminated by carrying this bit of parasitic soul."