As others have said, whether or not you can leave the 4" squares unquilted depends upon the batting you are using. However, if you decide to not quilt in the squares, you will have lots of 'stops and starts" or will have to turn your quilt to go around the squares which you might find is difficult or tiresome. I do lots of straight line and wavy line quilting with my walking foot, and find it is easier and looks great to just quilt from edge to edge on each line. I like my straight lines to be 1" apart.