What applique method do you plan to use?
When I do needle turn or freezer paper, I prefer not to wash -- I find the fabric with sizing on it is easier to handle and looks crisper.
Sometimes, with a fusible, I think it is better to prewash, but I don't have a firm rule on that. I just know that there are some fabrics (house brand of a very popular online /catalogue fabric source) that will visibly shrink when you press -- and you obviously need to press using a fusible. A tighter weave like a batik, I think you can get away with not pre-washing.
If you're doing a major project with a lot invested, consider doing a small sample with both unwashed and pre-washed, quilt them up, maybe as a potholder or a small zipper bag, and see how they fare after washing. If nothing else, you'll have an evidence-based reason for your choice as opposed to fear/worst case scenario basis.