I suppose anything is worth a try, the problems that you could going to run into is that the removal process usually stretches the sheet to the point that it's difficult to get it to lay flat again. You may also find that the years of exposure to light and normal houseold air pollution have faded the color of the paper so that the one in the closet won't match. The other thing that could be a problem is if the walls weren't prepared properly before the paper was hung. Papers that were hung over bare drywall or cheap paints and primers are a bugger to remove. Here is another catch that just crossed my mind, Pattern repeat. Will the pattern match up?
How you go about this will depend on the type of paper that it is. "Strings" and "Grass Cloths".....Forget it, don't even try it, they just fall apart under water. If it is a Fabric Backed Heavy Vinyl, it will just pull off the wall, and you hope that it doesn't take the wall with it. Then there are the two most common, the Peelable and the Stripable papers. The best for what you want is the Stripable one. Peelable papers will separate, leaving a backing on the wall while you peel the vinyl facing off. These can be taken in one piece, but you have to be really carefull. Stripable papers do not peel so they have the best chance of being rewetted and removed in one peice. Here is a trick I have used to remove sheets intact:
Using a large sponge or a small trigger sprayer, I wet an area of the wall and spread paper toweling over the wet area, then move on and do another area, repeating until the entire sheet is covered with wet paper toweling. I then use the trigger sprayer to keep the toweling wet for 15 to 20 minutes. I'll test the sheet at a bottom corner to see it the paste has released. If it hasn't, carefully smooth the toweling back down and wet it again for a few more minutes. Eventually the paste will soften enough for you to remove the entire sheet in one piece.
Take the sheet imediatly to a working surface and apply adhesive to the back and hang it in place of your damaged sheet.