I have used my embroidery module on my machine and used both WSS and no stabliizer.
I used the WSS when I was doing some feathers, and I needed to align the next design with the first, this was the way it was taught in a class on Quilt University. The WSS wasn't because stablizer was needed to stablize the quilt, but rather, as something to sew some alignment lines onto, then place the quilt on those lines, so the next design would sew where it was supposed to.
I also just finished a quilt where I embroidered a quilt motif rotated around in each block, and used no stablizer. Since the quilting designs are just outlines, you really don't need the stablizer. I had already layered and basted this quilt together, before I decided on how I wanted to quilt it. So I just hooped all three layers in my hoop, and lined up the design where I wanted it to stitch out and it looked great.
Do some tests with your top fabric, batting and backing fabric, and see how it turns out, if you like it with or with out the stabilzier.
Diane in Colorado Springs