We know that if you (using Polyjuice), take the form of someone who had been injured, you assume that injured form (e.g. Barty/Moody). If you are injured, presumably you would be uninjured while under Polyjuice. My question is, is this in real-time? That is, if you take a Polyjuice, and while you're still under its effects, the person being transformed into gets injured (or even dies), will that injury be transferred onto you? And conversely, if you get injured while in someone else's body, will that transfer over to your real body after the Polyjuice wears off, will it disappear, or will it go to the person you turned into?
Lets take the account of Moody and Barty Crouch Jr and use it as an example/reference.
Barty is using polyjuice potion all year long, with no apparent change in weight or hair.
below, apparently fast asleep, thin and starved in appearance, was the real Mad- Eye Moody. His wooden leg was gone, the socket which should have held the magical eye looked empty beneath its lid, and chunks of his grizzled hair were missing.
So here we see that the real Moody has been loosing weight due to 8 months of imprisonment, and also has an extremely sloppy hair cutting job.
Yet Crouch retains Moody's pre-sick appearance, and pre-cut hair. So this proves firstly that injuries that happened to Moody after the hair was cut(including the haircut itself) did not effect Crouch in real time(while under the effect of the polyjuice potion), NOR do those injuries appear to effect polyjuice potion made with hair before the weight-loss/haircut, or polyjuice potion made with hair after the weight-loss.
Only permanent damage seems to be conveyed through the polyjuice, scars, missing leg, ect but status like weight, and hair are not.
To answer the second part of your question, no injuries to the person who is under the effects of the polyjuice potion has ever shown up on the person whose hair or other was taken from.
Mrs Weasley had staunched his bleeding now, and by the lamplight Harry saw a clean, gaping hole where George’s ear had been.
Here we have George getting injured while under the polyjuice potion to appear as Harry, yet Harry does not ALSO get his ear injured, And the injury persists on George AFTER the effects of the polyjuice potion wear off.
I do not believe there's any reference showing that it is in real time. You only essentially take the shape of another person, it's not meant for you to be an exact clone where whatever happens to them happens to you.
Polyjuice Potion is a very complicated potion that allows the drinker to assume the form of someone else.
You do however retain the transformed state after you die while under the effects of Polyjuice though, which is what Barty Jr's mother did to save him. Now we don't know 100% if you keep the form forever after you die, but you would at least keep the form for the hour it takes for the potion to wear off.
Both mother and son drank Polyjuice Potion to take each other's appearance, and she went to Azkaban while Barty Jr. went to live in hiding with the help of their House-elf Winky. Mrs. Crouch drank the remaining potion slowly and sparingly, to ensure herself not to be exposed for the other prisoners to see, and died shortly thereafter in Azkaban. She was buried by the Dementors outside the walls under her son's name and appearance, as Sirius Black witnessed.
So essentially it is not real time because if it was then Barty Jr would have died when his mother passed away while under the effects of the potion. Also consequently, I believe if you are injured while under Polyjuice the injury would only transfer to your regular body at the area you were injured.
One must recall that Polyjuice potion requires part of the person being imitated, e.g a strand of hair, just before being drunk. I would presume that this part 'encodes' (magically or otherwise) the appearance of that person at the moment it was taken from that person. Therefore anything that happens to that person while being imitated does not affect the appearance of the imitator.
Now this raises the question of how Barty Crouch Jr managed to look the same while Alastor Moody was wasting away. Possibilities: (a) Barty pulled an adequate supply of hairs to last several months (and the follicles don't have to be alive for the Polyjuice to work); (b) Barty was able to make his face look more normal with magic, or even simple make-up (or maybe even Moody's deterioration didn't change his face too much), and covered the weight loss by padding his clothing.
Basically the Polyjuice potion allows an individual to assume the appearance of another individual at a given moment that is if Barty Crouch Jr Had tortured Alastor Moody his "polyjuice appearance" wouldn't change until his reserves ran out and he had to brew a new batch with fresh hairs that would include the new injuries.
What you describe in your post pertains more to what could happen if a "wound sharing/ wound transferring curse" was involved of if your future-self tortured your present self, see the movie "Looper".
However I've been wondering for a long time if Polyjuice can be used to prevent death from grievous wound until medical attention can be provided, or temporarily cure impairments such as blindness,or Deafness?