This one is a bit tough as it greatly depends on how you think of the problem.
Materials can respond very differently depending on how you measure them for strength. There are around a dozen common factors of strength given to each material. Each of which describes how weak or strong a material is in different tests.
Paper for instance is very strong if you try to pull it apart - So strong in Tension, but it crumples or folds up if you push two sides of the paper together - So weak in Compression.
You can also twist things, tear things, bend things, support weights. Some things can withstand a bullet, but if pulled slowly will fall apart. I will address paper Tension (pulling apart) below.
If you take a piece of paper, crumpled or not, and try to pull it apart you will find it very difficult. So in that way it is really strong. I believe the main thing crumpling the paper would do is to put a defect in the paper, which makes it easier to rip apart.
For example, take a piece of paper and fold in half. Press down on the crease, then fold the paper the other way and again press down on the crease. You will then find it much easier to rip the paper along the crease. By crumpling up a piece of paper, you are in essence making many small creases that rip more easily that the rest of the paper. So it will be weaker because you're making places in the paper that tear easier. These creases would weaken the paper in several of the possible tests for strength, but probably not all of them.
Hope this answers your questions,
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