Yes this system is plausible, but:
It's much more likely to evolve in natively aquatic species with singular circulatory system not divided in systemic and pulmonary circulation (maybe branchiary circulation here), because in divided circulatory systems main gas exchange organs are always relatively close to a heart, and having them in the neck would make it an even more vulnerable area with 2 arteries (at least) and a pair of gills with huge amount of blood flowing through them, ready to be ripped apart by predators or other merfolk (yes i know that gills in the neck are vulnerable enough without arteries, but i would really prefer to have my jugular cut OR lung punctured and not both at the same time)
I don't think it is as plausible for terrestrial species adapted to aquatic environment, because every stage of evolving a new organ must be beneficial to an organism, and creating completely new gas exchange organs seems much more demanding than adapting existing ones.
Personally i would use one set of retraced/retractable gills supported by breathing through skin, like a mudskipper. But since you want separate organs for breathing on land, i would suggest a second set of gills set into the chest, maybe even completely retracted inside a body, without slits, but with a set of orifices, limiting their drying. This would work fine with undivided circulatory system and doesn't look very out of place, just two sets adapted to different environments. Land gills could still support water gills while submerged, maybe even pumping water in and out themselves by muscular contractions.
I hope i helped.