The only drawback that I can see is scrunching the quilt up it's bound to mess up the applique before you have a chance to quilt it down. Also, the idea to do the overall quilting first is a really great idea. The class I'm taking now has us doing one block at a time backed with battilizer. We start with a 14" square, do an overall grid and then position the raw edge applique and use decorative stitches which goes through the top and the battilizer to attach the applique. It's nice to not have to worry about starting and stopping the quilting grid. We use paper backed fusible. If I have several layers, like in a flower, I will use the technique taught by Fons and Porter. (Which entails cutting the bulk of the fusible out and leaving a rough quarter inch around the edge of the applique.) After all the applique is done, I then trim down to 12 1/2" square. When it comes time to sew all the blocks together, I think I will not use batting since I will have all that battilizer in it. In that case, I will just quilt on the sashing.
Would love to see a picture when you are done.