I will often stuff an applique if that is the look I want. You do want to keep stuff light, don't want to have to over-dry the entire quilt when you wash it.
In this top which I'm keeping for my own grandbaby for when he is a little older, I stuffed the fish first and then quilted down through the fish and the full batting. I don't have very good hand skills and worse vision, so I prefer to set my stitch down to tiny and sew together my focus fabric along with some sort of backing, in this case I used a very thin batiste type fabric but I also use interfacing. Carefully cut a slit on the back and turn the whole thing right side out. Position and stitch in place.