Just my opinion....but i always stitch my appliques down and then stitch around them when quilting. I want them to be well secured to the background....and i can make "design" (using the word loosely here) choices about how i want the quilting to be afterward. Also...i quilt with my walking foot - and it is harder to see using that when trying to keep right on the edge of the applique to sew it down. I have a clear standard foot for that. Your quilt, your choice really. Either way will work.
Love your wall hanging !!!!