I have pulled about a dozen using my SS. All were hardwoods, up to 8" diameter a foot above the ground - some oak, maple and birch and one very stubborn cherry. Hickory or anything with a deep tap root will present some real problems, but the SS can get you started. You'll just need to find a way to sever the tap root before you can actually pull it out, but you can loosen it up real good before you get to that step.
One of the greatest difficulties is that half the time the stump will be right where you want to put your rear tire so you can rip out the lateral roots, so I cut the stump off low to the ground. This eliminates the option that ericher69 described, so think about it before you commit to this path.
If you can get to all sides of the stump, then you have a good shot at getting it out by cutting the laterals from a few sides, then hooking the stump and lifting to "pop it out" with the 3 point. Good 3 point lift capacity will help with this last part.