Yes, theoretically it is possible. Two possible scenarios: 1. You are young and healthy. You have mild lung inflammation from a virus but a lot of reserve. You may or may not have other symptoms, but from respiratory standpoint you will not exhibit symptoms until you get over your reserve as you would when you exert yourself.
Another scenario, is similar to asthma. Lung inflammation can make your lung tissue more sensitive . You may no longer have a virus, but for several weeks after you recovered you could manifest shortness of breath on exertion because of sensitivity of the airway. I hope it answers your question.
Another scenario, is similar to asthma. Lung inflammation can make your lung tissue more sensitive . You may no longer have a virus, but for several weeks after you recovered you could manifest shortness of breath on exertion because of sensitivity of the airway. I hope it answers your question.