I always pin anything I'm blocking. The curling will pretty much disappear once the piece is seamed, regardless, but you can elim some of it, perhaps. As you know, st st naturally curls but if you can reduce the amt of it before seaming that might be helpful. (Sometimes the amt of curl has you fighting to undo it as you seam.)
BTW, natural fibers benefit more from blocking. What is the yarn in your stocking?