All gamebird hybrids are sterile because they are all taxonomically distinct, in fact, gamebirds (order Galliformes) are split into nine extant families: Megapodiidae (Megapodes), Cracidae (Curassows, Guans, Chachalacas, and Pollopavo), Numididae (Guineafowl), Rollulidae (Roulouls), Phasianidae (Pheasants, Monals, Yejakuns, Tragopans, and Sonakebaters), Odontophoridae (New World Partridges and Quails), Perdicidae (Old World Partridges and Quails), Tetraonidae (Grouse, Turkeys, and Koklasses), and Gallidae (Chickens, Shizurens, Francolins, Spurfowl, Senlinaos, Ropohons, Jinegus, Daoiren, Peafowl, Arguses, Nartakees, Wajameras, Rohutans, Snowcocks, Chungchis, Alavorona, and Shabalrimals).
Yes, Rooster over golden hen will have better chance than golden male over chicken hen, with ring necks you’ll have better luck using a ring neck roo over golden hens.