I'd do it, but I would remove it from the hoop to trim the batting. Just mark the center lines to get it lined back up.
There are some designs that I'd hesitate to do that, but I think this one you could with good enough results. And if you only did the puffy part with the center motif, it would be a lot less challenging to get it lined back up. Finding a design that was intended for applique would be the easiest to start with.
I would also float the batting and top fabric. I'd only hoop the stabilizer. If you keep everything tight and flat, you may not get much "poof"
I've done shadow trapunto on a regular machine - using water soluble thread for the initial sewing of the batting - then you cut the batting and stitch it to the background fabric.
I'd also think that if you just did this with a high loft batting, you may get similar results as the open area of the center is going to be more poofy than the densily quilted area around it.