Is there any possibility that Harry's wand was a Horcrux?

Question

I came upon this possibility due to Dumbledore's words:

“I believe that your wand imbibed some of the power and qualities of Voldemort’s wand that night, which is to say that it contained a little of Voldemort himself. So your wand recognized him when he pursued you, recognized a man who was both kin and mortal enemy, and it regurgitated some of his own magic against him, magic more powerful than anything Lucius’s wand had ever performed. Your wand now contained the power of your enormous courage and of Voldemort’s own deadly skill: what chance did that poor stick of Lucius Malfoy’s stand?”

I feel that this is very much similar to the conversation between Harry and Dumbledore describing Voldemort has passed a bit of himself to Harry. The fact that Harry's wand was broken before the death of Voldemort also seems to support this. Of course we are told that it was broken by some mistake by Hermione but as it is not explicitly mentioned, what if it was broken by some irreparable means (maybe Nagini's venom) and Hermione misunderstood it to be caused by her? So my question is; has there been any discussion (either by JKR herself or any fanfiction) on this? Has it ever been brought to notice?

Answer 1

No, Harry’s wand didn’t have a piece of the Dark Lord’s soul in it.

Harry’s wand absorbed something of the Dark Lord when their wands connected, but not a piece of the Dark Lord’s soul. Dumbledore means that Harry’s wand absorbed some of the Dark Lord’s style of magic which his wand would have learned from him and contained a bit of - his skill and power.

“I believe that your wand imbibed some of the power and qualities of Voldemort’s wand that night, which is to say that it contained a little of Voldemort himself. So your wand recognised him when he pursued you, recognised a man who was both kin and mortal enemy, and it regurgitated some of his own magic against him, magic much more powerful than anything Lucius’s wand had ever performed. Your wand now contained the power of your enormous courage and of Voldemort’s own deadly skill: what chance did that poor stick of Lucius Malfoy’s stand?”
_{^{- Harry Potter and the Deathly Hallows, Chapter 35 (King’s Cross)}}

Wands absorb some of the experience of their owners, so the Dark Lord’s wand would have learned from him and have a bit of his specific power and skill. This is the ‘part of’ the Dark Lord that Harry’s wand imbibed from his wand when they connected - the magic it learned from him.

The Dark Lord’s soul only broke since the Killing Curse hit him.

Also, nothing happened to the Dark Lord that should have caused a piece of his soul to break off and separate. The last time it had happened was when the Killing Curse rebounded and hit him.

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself on to the only living soul left in that collapsing building.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

The Dark Lord wasn’t ripped out of his body by the Priori Incantatem, nor was he hit by a Killing Curse, so it shouldn’t have broken off another piece of his soul.

Bits of soul that ‘break off’ only attach to living souls, not objects.

Furthermore, if a bit of the Dark Lord’s soul broke off, it couldn’t stick itself in Harry’s wand. As shown by the one in Harry, pieces of soul that break off and aren’t intentionally sealed in a Horcrux can only attach themselves to living souls, not inanimate objects.

“Tell him that on the night Lord Voldemort tried to kill him, when Lily cast her own life between them as a shield, the Killing Curse rebounded upon Lord Voldemort, and a fragment of Voldemort’s soul was blasted apart from the whole, and latched itself on to the only living soul left in that collapsing building.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)}}

The piece of the Dark Lord’s soul attached itself to Harry because he was the only living soul there. Harry’s wand is a wand, not a living soul, so even if a piece of the Dark Lord’s soul broke off somehow, it couldn’t possibly attach itself to Harry’s wand.

Answer 2

Harry finds contact with horcruxes — the locket, the diadem, even his own scar — to be disturbing, even painful. To a lesser degree, contact with unsuitable wands also feels wrong.⁽¹⁾

With those two tells, Harry would likely have known if something was dangerously — such as it being a horcrux — wrong with his wand. Since Harry's phoenix-core wand always seemed "right" to him, from the moment it chose him until after the last trace of Voldemort left Harry, it seems that the wand remained uncompromised.

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⁽¹⁾ "[The blackthorn wand] felt intrusively unfamiliar, like having somebody else’s hand sewn to the end of his arm." (Deathly Hallows, Chapter 20: Xenophilius Lovegood)