Can reflux cause mild edema of lungs?

Not edema : Pulmonay edema usually means increased interstitial fluid as a consequence of fluid overload (ie chf). That is not a consequence of gerd. Regurgitation of stomach contents may make its way into ones lungs if severe enough and patient unable to clear it by coughing. These aspirating events may cause focal inflammation of the lung.

Reflux can hurt lung: I am not exactly sure what you mean by long edema but stomach juice that comes up and gets into the throat and spills into the lungs can cause significant damage. The damage certainly can cause swelling and edema of the lung tissue and can lead to pneumonia and pneumonitis.