Are the old comforter and the new one the same size? I'm wondering if you can harvest the top from the old one and sew it to the new comforter. Can it be attached right sides together, sewn at the edges, turned right side out, then tie it instead of quilting it? I think this might be what you are suggesting. Like CathyD, I question being able to get the new comforter under the presser foot.
If the old comforter was quilted together, getting the top off is going to leave stitch marks. It might be better to simply patch the missing batting in the old one and put a new back on it.