Hi and welcome to the board!
I have never tried this and I think it could work, but I would be concerned that the areas of the quilt that have no batting (wadding) may shrink differently then the rest of the quilt and will most likely wrinkle horribly in the wash. The wrinkling can be ironed out, the uneven shrinkage, not so much. I think I would do a mock up on a much smaller scale, like say placemat size or table topper size and see how it works.
The other consideration is how you would finish the piece. Obviously you would need to quilt and sew to completely encase the batting but such a thin edge where you don't have any batting, may not work so well for a traditional finish of a quilt with binding. You may have to do a knife edge finish. Again, you won't know until you try it so another good reason for a much smaller scale mock up.