I was just reading Harry Potter and the Deathly Hallows, and I was wondering, when Hermione Granger changed into Bellatrix Lestrange, she should've obtained the Dark Mark, temporarily.
Now, my question is: would the Dark Mark work if pressed?
Would there have been a Dark Mark?
I'm inclined to say yes. When Barty Crouch transformed into Moody, the transformation removes the limbs and body parts that have been severed. So the potion does seems to include external modifications to someone's physical appearance, not just a clone based on their DNA or something like that.
More to the point, when Ron drinks Polyjuice Potion to transform into Harry, he says the following:
...which is a pretty good indication that tattoos are included in the transformation. He was, after all, standing next to Hermione, who no doubt would have leapt to correct someone's deficient knowledge of magic.
Would it work? I don't think there's enough evidence in the books to say one way or the other. But my guess is no.
As an analogy, we can assume that the Seven Harry Potters all had Harry's scar, or else the plan would have been worthless. But obviously, not all of them were screaming in pain or losing consciousness when Voldemort approached them. All of them received the external properties of Harry's scar, but certainly not the magical powers associated with Voldemort's soul.
Here's the description of the Dark Mark from Snape:
Given that the Dark Mark gives the wearer the ability to instantly know Voldemort's location, and is created personally by Voldemort, I doubt the Dark Mark's power would be duplicated so easily. If so, it would have been child's play for an Auror to be constantly transformed into a known Death Eater, wait for a general summon, and Side-Along Apparate an elite Hit Squad to Voldemort's location. I just think Voldemort's far too clever for that.
To clarify, I think what Ron meant when he said "I knew Ginny was lying about that tattoo" is that Ginny had been playing a joke on Ron by telling him Harry had a tattoo, when Harry actually didn't, and never had had a tattoo. I do not think it suggests that tattoos wouldn't be replicated through Polyjuice Potion.
I think canon is clear that Polyjuice Potion gives a person the exact appearance of another, as they are at the moment the Polyjuice is taken. It even makes a person sound like the person they turn into; a person adopts the other person's voice. Tattoos and the Dark Mark would ostensibly also replicate onto the person taking the Polyjuice Potion.
I think it's more likely that a Polyjuice Dark Mark would not actually work like a real Dark Mark. As I mentioned, Polyjuice recreates physical characteristics of another -- only appearance. It does not enable magical abilities that were not presence prior to the taking of Polyjuice to suddenly manifest. To give an example, Harry could Polyjuice into Dumbledore -- he would look and sound like Dumbledore, but he wouldn't become the prodigious wizard that Dumbledore is. He would retain the magical skill level of a teenage wizard. Harry would retain his own magical essence.
Presumably, Mrs. Crouch would have taken on Barty Crouch Jr's Dark Mark in Goblet of Fire:
This example is difficult because, again presumably, Mrs. Crouch should have received Barty Crouch Jr's appearance, and she did -- only his appearance, for she remained ill and died under Barty Jr's appearance. But here's what's weird:
Polyjuice affects appearance only. When Barty Crouch Jr Polyjuiced into his mother, it's unclear why he also manifested her terminal illness, which the Dementors sensed on him. If this were to be true, it seems that Mrs. Crouch should have, in turn, become disease free, as Barty Jr had a healthy body. But this didn't happen -- both manifested Mrs. Crouch's illness.
Accordingly, we can't discount the possibility that a Dark Mark obtained via Polyjuice might be functional, if the person sporting the Dark Mark knew what it was and how to activate it.
To sum, I think there are more instances of Polyjuice demonstrating Polyjuice affects only one's physical appearance. However, the Crouch incident with Barty Jr and his mother opens the door to the possibility that a person may take on more than physical appearance when drinking Polyjuice. I think the latter is remote -- very remote -- but, hey, J.K. Rowling left a little room for interpretation there.
ETA: To address an issue that arose, that Barty Crouch Jr was dying in Azkaban, canon does not state this outright:
Sounds like Barty Jr was definitely sick or weakened, but Goblet of Fire does not say -- and we should be careful inferring -- that Barty Jr was on death's door. It's possible he was, but canon does not explicitly state this. Azkaban would not have treated any of its prisoners kindly.
Originally, I wasn't going to address this, but, as it turns out, it needed to be.