Could inhalation of chlorine gas cause pulmonary edema?

Yes. Typically happens upon exposure to chlorinated bleach fumes. The reaction in the lungs can range from mild to severe requiring life support. More likely to happen in asthmatics. Best is to avoid using chlorinated products, or use in well ventilated areas, preferably wear a mask.
Absolutely. Chlorine gas is extremely toxic to the lungs with inhalation and frequently fatal. It damages the fragile alveolar capillary membrane and causes fluid to leak into the air spaces.

Related Questions

Why can pulmonary edema cause shortness of breath?

Gas Exchange. Pulmonary edema affects the flow of oxygen from airsacs / alveoli to blood vessels in the lungs called capillaries. This is called gas exchange and results in low oxygen levels. Read more...
See below. Pulmonary edema means swelling, or filling of the lungs with liquid. When that happens, the lungs cannot perform their physiologic function which is to exchange oxygen and carbon dioxide between the blood and the air we breathe. The air doesn't get to the alveoli because they are filled with liquid. That is how one gets short of breath. Read more...