Nagato doesn't have chakra chains. He can only use the chains granted by the gedo mazou but that requires him actually summoning the mazou, it'll then cripple him like it already did in the past the first time he summoned it.
Bringer of Darkness isn't getting sensed, and its not a visual genjutsu, it's a genjutsu than renders "the senses" useless. Hearing & Vision. The third hokage could only combat it with his accute sense of smell granted by knowing Inuzuka clan techniques.
And considering Hashirama lived
You must be registered for see links
I see Hashirama having no trouble surviving CST, not to mention he can summon Rashomon gates too.