It would absolutely in the Soviet's interest to make sure people know that the weapon exists -- it helps keep them alive! To paraphrase Dr. Strangelove, what's

It would absolutely in the Soviet's interest to make sure people know that the weapon exists -- it helps keep them alive! To paraphrase Dr. Strangelove, what's the point of the doomsday device if they don't know you have the doomsday device? I agree with your assessment that NATO intel probably knew of it, but kept quiet to avoid political drama and keep sources secret.