Can Polyjuice Potion change someone who is "dead" into someone else, or does it only work on living wizards and witches?

We know from Harry Potter and the Goblet of Fire that dead people stay in their transfigured form as Barty Crouch's mother died and was buried as him:

“My mother died a short while afterward in Azkaban. She was careful to drink Polyjuice Potion until the end. She was buried under my name and bearing my appearance. Everyone believed her to be me.”

^{*Harry Potter and the Goblet of fire, Chapter 35 - The Madness of Mr. Crouch}

But we also know, that one needs to drink the Polyjuice Potion for it to start working. I have no idea how you would make a dead person drink the potion.
That's why I don't think it's possible to change a dead persons' look via Polyjuice potion.

EDIT: to answer the additional questions from the comments: what makes medicine (or alcohol) effective after drinking it? It becomes active by being digested or absorbed. I don‘t think that this process still works in a dead body. And I personally imagine the effect of a potion that has to be drunken to be the same: no digestive activity, no effect. So just magically put the potion into ones stomache should not make any difference...

No, because dead people can’t drink the potion.

Every time someone uses Polyjuice Potion to transform into another person, they have to actually drink the potion. It only starts transforming them after they swallow it.

“Pinching his nose, Harry drank the Potion down in two large gulps. It tasted like overcooked cabbage.

Immediately, his insides started writhing as though he’d just swallowed live snakes – doubled up, he wondered whether he was going to be sick – then a burning sensation spread rapidly from his stomach to the very ends of his fingers and toes.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 12 (The Polyjuice Potion)}}

Since dead people can’t swallow, and there’s no indication that it’ll work if it just makes contact with the person, but they don’t actually drink it, it’s very likely Polyjuice Potion won’t have any effect on someone who’s already dead before the attempt to give them the potion.

In addition, it seems likely they need to be alive to transform.

Even if the Polyjuice Potion was shoved down the dead person’s throat, it still almost surely won’t work. It also seems like the person using Polyjuice Potion needs to be alive to transform. Barty Crouch Jr.’s mother had been using it to transform herself into him, but when she died, she didn’t turn back to herself - she stayed as Barty Crouch Jr. even though the potion should have worn off.

“My mother died a short while afterwards in Azkaban. She was careful to drink Polyjuice Potion until the end. She was buried under my name, and bearing my appearance. Everyone believed her to be me.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 35 (Veritaserum)}}

Though the Dementors themselves are blind, Sirius saw Barty Crouch Jr. being buried from inside Azkaban, and saw the corpse as him, not his mother.

“Crouch never came for his son’s body. The Dementors buried him outside the fortress, I watched them do it.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 35 (Padfoot Returns)}}

Since Barty Crouch Jr.’s mother didn’t transform back after using Polyjuice Potion and then dying before it wore off, it seems likely that Polyjuice Potion won’t work to transform a dead person.