Depends on the cookies.
Baking soda reacts only with acids. If your cookie dough is not acidic, baking soda will not produce any gas, and therefore will not provide any leavening.
Baking powder contains both baking soda and a powdered acid. When combined in a liquid the acid reacts with the soda and produces gas. If the cookies already have acid in them, I imagine that the additional acid from the powder will make the cookies bitter.