i've quilted lots of raw-edge applique quilts on the long-arm---why would it be questionable?
or are you confusing quilting with stitching your appliques down?
2 different things- raw edge applique simply means the edges are not turned under- usually *but not always* fused to hold in place- then secured with stitching- either a blanket stitch, zig-zag-satin stitch or even a straight stitch. quilting holds your 3 layers together- enhances and finishes the quilt design.
some people do thread painting with their long-arms.
you can do it any way you want that gives you the results you are looking for