Does the Polyjuice Potion Dark Mark work?

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:

Crouch took a deep, shuddering breath, then began to speak in a flat, expressionless voice. ‘My mother saved me. She knew she was dying. She persuaded my father to rescue me as a last favour to her. He loved her as he had never loved me. He agreed. They came to visit me. They gave me a draught of Polyjuice Potion, containing one of my mother’s hairs. She took a draught of Polyjuice Potion, containing one of my hairs. We took on each other’s appearance.’

_{Goblet of Fire - page 593-594 - Bloomsbury - chapter thirty-five, Veritaserum}

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:

‘The Dementors are blind. They sensed one healthy, one dying person entering Azkaban. They sensed one healthy, one dying person leaving it. My father smuggled me out, disguised as my mother, in case any prisoners were watching through their doors.’

_{Goblet of Fire - page 594 - Bloomsbury - chapter thirty-five, Veritaserum - Barty Crouch Jr to Dumbledore}

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:

‘And what did your father do with you, when he had got you home?’ said Dumbledore quietly.

‘Staged my mother’s death. A quiet, private funeral. That grave is empty. The house-elf nursed me back to health. Then I had to be concealed. I had to be controlled. My father had to use a number of spells to subdue me. When I had recovered my strength, I thought only of finding my master ... of returning to his service.’

_{Goblet of Fire - Page 594 - Bloomsbury - chapter thirty-five, Veritaserum}

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.