They sure do and so do Cherry Lynn and all the other thin dies. but if your plates start getting warped you may have to get new plates. I have one set of plates that are so warped that they don't cut very well any more.
They also include the directions for several machines, including the Big Shot/Big Kick, inside the packaging of each set of Spellbinders, which is nice, so I don't have to look it up every time I use them (I have only two sets, so I don't use them very frequently).
Actually many of the Grand Nesties do work in the Big Shot - e.g., Labels 11, Labels 4, Large Labels - as well as most of the dies in all the sets. It's only the very biggest ones that exceed 6-1/8" that won't work. Of course, I'm not saying you should buy a set of Grand Nesties if you can't use all of them, but don't rule them out completely since some of the sets will work just fine