I don't have a M&P 9 to try it with, but I'm guessing it won't. For one thing, the barrels on the M&Ps are different lengths...the FS is 4.25" and the compact is 3.5"...while the SD has a 4" barrel. Second, the take down levers are different, as well as other mechanisms. They are different guns.
None of this is a professional opinion, and may be pure hooey, but that's my answer. Maybe someone who has both can respond, or who knows more than squat.