You should probably check with your longarmer.
I know of some who have received the trapunto already done. By that I mean element you wanted the extra layer of batting was stitched around and the excess batting already cut away. And I do know that it was done by hand. The client appeared to have stitched the batting down at the same time as doing the applique.
So it can be done, but the question is does your longarmer have issue with it. Also don't forget you can't wet the thread or your needle eye (as we so often do by sheer habit) when threading the needle when you are using water soluble.