Could you have emphysema without coughing?

Yes: COPD could present with cough, frequent episodes of bronchitis, wheezing, or shortness of breath.

Yes: In the early stages, you can compensate for emphysema and have no symptoms at all. Later on, you may just have shortness of breath and fatigue without much coughing. Check yourself or your loved one, there is evidence that with early treatment the progression of emphysema may be slowed down.