burning methane does produce NO and NO2 (the N2 being oxidized at temperature). that does come down with precipitation and collect in bodies of water. over time as evaporation removes the water and its replenished with acidic rain, the concentration increases arbitrarily high.

idk how much NOx a GW or two of low efficiency (20%) gas turbine units produces, how wide that plume might be, and what the envionmental impact might be. but if we employed a few people that practice doing this kind of I'm sure they could tell us with high confidence.