I guess not, based on this experience. At least not in a washing machine/dryer.
I know for garment sewing, you really, really do need to pre-wash fabric (or calculate shrinkage). And yes, I’ve heard of hemming fabric before you wash it (and even done it, for a few precious fabrics). But fat quarters? They’re so small, I thought hemming before washing was a bit other the top.
By the way, no sympathy needed: I don’t mind detangling and they’re all separate and neatly folded now.