I'd say try a sample and see. I'm doing a crazy quilt with all machine stitched fancy stitches. It's on a foundation, and I've not had any problem not using other stabilizer underneath. The wider your satin stitch, the more likely you'll need stablizer.
One thing I learned from doing a stained glass looking project - overlap the pieces. I had cut to butt them up, and ended up with areas I had to go over, as I didn't catch both pieces of fabric. But that is another reason to do a test, you figure out what isn't going to work! BTW - I almost never go off directions so I have to learn the hard way.