Things to mention, it actually adds a noticeable weight to the edges which I rather like, sort of helps the edges to spread out when you put it on the bed. Watch to see if the cording does have any sort of natural drape or inclination to move in a certain way -- if you fight it, it will win in the long run!
I was concerned about long arming over the cording and only did the "bed" of the quilt on the long arm. Then I scrunched the couched border though my little old vintage machine and had zero issues. Silly me, I should have at least tried it on the long arm!
Back in my garment sewing and costuming days, I often did various couched techniques for braids and trims and have used feet to do it. Depending on the thickness I often use a matching color thread and zig zag.
Just as an aside, those old treadle machines and early electrics typically had all sorts of fancy feet and what the heck does this do items, and they are mostly helps to put on or make trims of various sizes.