You could couch a cotton yarn over the seam, it would go thru your embroidery, but if done on all the lines it will become a design element. Other yarn alternatives would be thin ribbon, or turned fabric tube, like for a spaghetti strap, made from same background fabric. I think the tube from the same fabric would be the least noticeable.
This is how I make mine. Quilting cotton is heavier than the fashion fabric she is using, so you will have to make the tube a bit wider. Working with shorter lengths is much easier than trying to turn a single tube for the whole project.
http://www.youtube.com/watch?v=muPk3tXV4I0