Does God ever use secular leadership to accomplish His purposes? If so, how and why?
Yes He does. For one, much of secular leadership teaching is based on biblical models. There are certain principles that simply are effective, whoever uses them. God is also not limited to accomplishing His purposes only through believers. Obviously God has used non believers, pagan kings and generals and even animals to accomplish His will! Sadly, there are unbelievers who have a better grasp on leadership practices than many Christian leaders have. Just because you are a Christian does not necessarily make you a good leader!
I think we sometimes feel that God is limited by man’s will. We cannot prevent God from accomplishing HIs will. Think of how Christ was planned before the foundations of the world to redeem mankind, yet over thousands of years of man and Satan trying to interfere, God’s will prevailed. No we are not robots, but we give ourselves too much credit sometimes. God can and does use secular leaders, and people who are not leaders at all, to accomplish His purposes. It is always best for us to be in the center of His will and allow Him to guide us in our obedience to Him so He can accomplish through us what He desires.