I have had severe lung problems for years, and my doctors (asthma/family) have pushed me to have the Nissen Fundoplication surgery. I also had a hiatal hernia, which I suspect pretty much all GERD sufferers do.
Anyway, keeping in mind that I had an asthma-induced lung infection before surgery, that continued after surgery, then caught the flu, I can't say I've been lung problem free since my surgery on 2/27, but I can tell you that the overall health of my lungs has improved markedly. I'm still coughing up green gunk, due to the fact that my asthma is not all GERD related, and my lungs overreact to anything that accosts them.
However, I can assure you that yes, GERD can cause lung inflamation, bronchial constriction, mucous production, and secondary infection.
If you are still coughing up green phlem, you should go in to see your doctor, to let him/her determine whether you might need an antibiotic.