I can't say for sure, as I've probably never tried whatever specific recipe you're aiming to use. The primary concerns are, if it has enough flour so that it's not overly sticky, and if it holds its shape fairly well during the baking process.
If the dough doesn't hold its shape well, (like if there's too much baking soda and/or baking powder in the recipe, or just not nearly enough flour) then they'll just end up as cookie-blobs in the end. If the dough is really sticky, it might be really hard to get it out of the cutter during use.
Add lots of flour to the cutter between each cutting, if you find you're having a lot of trouble with sticking.
As for recipes with large bits in them (raisins, chocolate chips, etc.) I've definitely seen cookie-cutter compatible recipes on various sites that say they'll work with cookie cutters. I haven't personally tried any of them, and if the cutter you're using has a lot of inner detail, the large bits could get stuck, or the detail could simply not show up because of the bits.