It really depends on the fabric you are using. Something very lightweight may need stabilizer. With something heavier might get away without it but I would use something.
It would depend on what type of effect you want. The washaway topper would keep the design from sinking down into the felt. Without it would mean the felt around the stitches would puff up a but and it would have a different look. Either way works - depending on the look you are going for.