Would lung reduction surgery help someone with bronchitis cough less?

No. Lung volume reduction surgery or lvrs is for patients with chronic emphysema, and not chronic bronchitis. Bronchitis is inflammation of the airways. Emphysema is loss of the elasticity of the lung tissue, and ballooning or air trapping of the lung tissue. Lvrs has proven (national emphysema treatment trial) to be beneficial and life saving in patients with poor exercise capacity, and emphysema in the upper parts of the lung.
Possibly. It is likely that the bronchitis contributed more to the emphysema leading to lung volume reduction surgery than the other way around. Control of the bronchitis is still required.