Would baking chocolate with baileys/kalhua cook out the alcohol?
With your plans, you have encoutered some questions and problems. Let's tackle one after another:


Alcohol boiling off
Although often repeated and assumed due to the lower boiling point of alcohol vs. water, alcohol will not boil off completely. Even after a long boil not only traces, but a significant amount of alcohol remains. There is a question and a bunch of answers here on Seasoned Advice discussing this. However, loosing some of the alcohol won't be a problem, the taste should remain (mostly) unchanged, unless the heat is so high that sugars - and both Baileys and Kaluha are sweet - start to caramelize. Your chocolate wouldn't fare well at high temperatures as well, so that's not the route to go anyway.
Alcohol / liquor and chocolate
Those two are unlikely to mix as long as the chocolate remains solid. Even after the chocolate has melted, you'd have to stir to incorporate the Baileys and be at risk of the chocolate "seizing", that is, getting lumpy. If you were thinking along the lines of whiskey truffles etc., those are made with heated chocolate + cream + liquor, then left to cool and solidify.
Soaking the "cake" or in this case the Graham crackers (as suggested by another answer)
Typically, one would expect additional liquor to be added to the baked goods, because they are "willing" to soak it up. Now as Skillet S'mores use the crackers to scoop up the soft chocolate-marshmallow mix, soggy crackers won't do. Unless you are planning to divide the crackers into individual serving bowls and spooning the mixture on top (or baking in individual cups with a soaked cracker base), that is not the way to go.


So what?

You want the alcohol to go into the chocolate. The only feasible way is to gently(!) melt the chocolate, either in the skillet (don't burn!) or in a bain marie (a bowl set over hot water). Use dry utensils and stir carefully, do not let small drops of water get into the chocolate. If possible, gently heat your alcohol, too. Add enough liquid to prevent seizing, that means go for at least one tablespoon per two ounces of chocolate, possibly more. If you feel that's too much alcohol, add some cream. Stir well. 

Pour chocolate into pre-warmed skillet (if not already there), cover with marshmallows, broil until marshmallows start to melt and bubble, enjoy!