Well, there are several answers to this question. The first is, yes, that was the plan, and that was the system that both nations set up. They were both ready to do it. Was it a bluff? No. There's no reason to think so. It was so not a bluff that there were concerns, including from within the nuclear weapons systems, that they'd set it off on accident very easily. These were immensely complicated, fully-staffed, 24-hour-a-day systems. Deterrence wasn't (and isn't) just an idea — it's an infrastructure. It's huge. The whole strategic concept doesn't work unless you are really prepared to do it, and the other side knows it.

The second answer is, well, it depends on the specific country you are talking about, because the authorization of a nuclear strike is not "automatic," per se. In the US it requires the explicit order of the President of the United States (except in certain "pre-delegated" situations). So let's say it is the 1970s or 1980s and NORAD detects Soviet missiles launching. A conference would have been quickly called with the President and his advisors, and ultimately the President would be asked whether to authorize some particular plan of retaliation. In the end, whether that retaliation happens is up to the President. Could we imagine an individual President saying, "don't reply, it's not worth it," or something like that? I mean, it feels unlikely. But it's not at all impossible. You're talking about an individual human response to a scenario that has never occurred. These are inherently unpredictable; they are not like gauging average responses over lots of people. Individual people are difficult to predict and understand. So sure, you could imagine that happening.

What about in the USSR? The Soviet system worked differently than the US one, from what we know of it. Nuclear use authorization in the 1970s was a system that required the Politburo to first transfer nuclear use authority to a top military leader. Then the top military leader became the decider on it. In the 1980s, they seem to have changed to something more like the current Russian system, in which the assent of several people were necessary to use the weapons (two out of three people need to approve a use order for it to be valid under the current Russian system). And they also deployed a "fail-deadly" system called Perimetr, which, if activated, meant that any loss of communication with Moscow would result in a launch order being propagated. So you can see that each of these systems very much changes our question of whether a nuclear retaliatory strike would possibly be used. Even the difference between two people needing to agree versus one is a big one (and it is not clear which of these scenarios is more likely to produce a use order, as an aside), and certainly the "automatic" system changes it a lot.

The third answer is, it really depends on the scenario and its context. The odds that one nation would decide to, out of the blue, launch all of its nukes at the other were already considered really low. Not impossible, because first-strike was never thought to be impossible (which is one of the reasons why MAD as a philosophy was not itself actually that popular among the militaries of either side — neither were just going for deterrence, they were looking for the possibility of dominance), but not the likeliest scenario. More like were escalatory scenarios in which both nations would try to avoid a "full nuclear strike" through lesser use. This was unknown territory for both sides and both feared it to various degrees.

Anyway. There is much more that one could say about this. The short answer is, both nations built systems, and strategies, around the idea of a guaranteed response. This is because they hoped that such systems and strategies would avoid the problem altogether, ultimately. We cannot really say what would happen in any given scenario, because the number of unknowns is huge. However it would be, I think, foolish to assume that it was "a bluff." The people manning such systems certainly did not regard it as a bluff. I think there is really no good reason to think that the weapons would not have been used against one another reciprocally, just like the systems were — and still are — designed to do.