I have never tried this, so I can't assure you that it will work. I wouldn't use a dense design, nor would I hoop the felt. I would hoop the stabilizer and use temporary adhesive spray (Sulky KK2000), or the basting function to adhere the felt to the stabilizer. I would also use a topper to keep the stitches from sinking into the felt.
You can successfully embroider on fleece. As for the felt, all you can do is give it a try. If you do, let us know how it worked, okay?