most won't, but some cotton batting will fall apart if you wash it all by itself. most cotton batting will shrink once it is washed. how much it will shrink varies by manufacturer. the good ones are honest about that and will tell you right on the package how much shrinkage to expect.
when batting of any type comes out of the package it's quite wrinkled and lumpy from having been folded so tightly for so long. working with it like that can be a bit of a pain where you'd prefer to sit. the solution is not to prewash it like you would fabric.
throw it in the dryer, on the delicate or knit setting, with one or two damp bath towels. the moisture from the towels will infuse the batting without weakening it. by the time the towels are dry, the batting will have done whatever shrinking it's going to do and come out in a smoother condition. it'll be easy to flatten out any remaining wrinkles or lumps.