Normally the quilting would be done after but several months ago (Possibly as long as a year) I read on another forum where the maker quilted before and it made everything much easier for her because she didn't have the constant starts and stops. She posted pics of the project and you could not see the quilting lines under the applique but this was not fusible, this was a turned edge applique that was prepared with seam allowance already turned under and then hand sewn to the quilted top. Fusible could be a problem if trying to quilt before adding the applique and then yes, I believe the quilting lines would show due to the nature of fusible.
Additionally, I believe the quilter ditched around the applique after adding it.