So like a full butterfly embroidery motif?
I would do those before the quilting. So just fabric and stabilizer.
I think it would work technically, but wouldn't look so great on the back.
However, if it's just one of the fancy stitches - like the hearts or vine, then you can do that with the batting/backing.
And that will look very cool on the back (if you use nice thread in the bobbin, that is).