If chemical reaction begins when baking soda/powder are added to cookie dough, how does chilling the dough (often recommended to re-firm the butter) impact the chemical leavening process?
This is pretty much echoing GdD's comment, but chilling dough generally slows the chemical reactions significantly. Since you are also talking about "dough" and not, say, "batter," the moisture content is likely lower. This is significant because it will also inhibit leavening reactions, since higher moisture allows chemical components to circulate more easily and thus can aid reactions.
Most modern baking powders are already "double-acting," which comes from the fact that they have multiple acidic components that begin to react most strongly at different temperatures. Baking soda (and sodium bicarbonate that is already part of most baking powders) will begin to react with acidic components already in the dough when mixed, but the other acidic components of baking powder will only activate strongly upon heating, at which point they will react with the remaining sodium bicarbonate (i.e., baking soda, whether added separately or as a component of the baking powder) to form gas bubbles.
In sum, if you're using a "double-acting" baking powder, the secondary reactions will be slow whether the dough is at room temperature or chilled. Chilling will inhibit initial reactions as well, but those are most significant in doughs that depend on baking soda and added acid in the recipe. However, I doubt most cookie recipes that depend on such leavening would include a chilling step, because leavening power will gradually be lost even at low temperatures.
I haven't seen this for cookie recipes, but I have seen biscuit recipes (for example) that use a bit excess baking powder while anticipating that the biscuits will be held in the refrigerator for a few hours (or sometimes even overnight) before baking. Although some initial bubbles may be lost, the heat-activated components of the baking powder still ensure a final rise in the oven.