crazy quilts are (traditionally) not quilted---they are generally tied---because of all the embellishments.
the traditional crazy quilt- blocks are created with different size/shape texture pieces-on a foundation- then every seam is covered with decorative stitching- all of the blocks are joined- embellishments are added- then a backing is added & tied then a binding.
but you do not have to follow the (traditional) method- if you want to use your decorative stitching as your quilting it would go through to the back-
and it probably depends on what you plan to use for embellishments how it would be best to go about that part...but a traditional crazy quilt is not quilted. the quilting would interfere with the decorative stitching & embellishing.