Catalyzes the reduction of glutathione amide disulfide (GASSAG) to restore glutathione amide (GASH) in the presence of NADH. May play a role in GASH metabolism under anaerobic conditions as a sulfide carrier necessary for cytoplasmic sulfide oxidation. 2 glutathione amide + NAD(+) = glutathione amide disulfide + H(+) + NADH Binds 1 FAD per subunit. Homodimer. The active site is a redox-active disulfide bond. Belongs to the class-I pyridine nucleotide-disulfide oxidoreductase family.