I did a simple Sunbonnet Sye years ago and I did not cut away the back. Are you doing traditional needle turn appliqué? If so then there shouldn't be too much fabric under the pieces and the machine should handle quilting though it. If it is several layers of fusible and fabric, yes you may need to machine quilt the outline only. I usually "window" large appliqués with many layers when doing fused machine appliqué.