1. Shortly after WWII, the atomic bomb being in the hands of the USA and Great Britain, Churchill developed a plan to invade the Soviet Union among other with the help of German SS troops. His "Operation Unthinkable" however was turned down by the British Army High Command for alleged exhaustion of British troops and uncertainty of the state of Soviet nuclear arms research. The intention however to invade the Soviet Imperium must be assumed to have persisted, because no change during the Cold War made it apparently unnecessary. It was only the Soviet nuclear armament which prevented such a strike.
2. During the Cuba Crisis an US Destroyer attacked a Soviet Submarine which was about to fire a nuclear torpedo in retaliation. The launch was prevented by one Russian officer, Vasili Arkhipov, refusing to turn his key.
3. In another incident in 1983 the Soviet radar early warning system in Moscow falsely detected an alleged nuclear first strike originating from the USA. It was the Russian officer on duty, Stanislaw Petrov, refusing to take the necessary steps to launch an early Russian counter strike according to the plan.
4. During the NATO maneuver "Able Archer" in 1983, which was a Western "hot exercise" and life simulation of a Soviet nuclear first strike, based on the intelligence received from NATO sources, the KGB and Russian government were 100% convinced that NATO itself would be preparing a nuclear first strike. Thanks to the mentality of the Russians they kept their nerves.
The USSR did not prevent a nuclear war/Armageddon with the United States as both countries worked equally (or mostly equally) to stock-pile weapons from the mid 1950s through the late 1980s. Evidence shows that both countries had stock piled a large nuclear arsenal over nearly 40 years and that both countries were each hesitant to use their weapons under the concept of Mutually Assured Destruction (MAD).
No, I do not think that the Soviet Union prevented a nuclear Armageddon with the arms race against the United States, because what prevented a nuclear Armageddon was the fact that the USSR broke down under Reagan. If it hadn't broken down, the arms race would have continued, eventually ending in war.
The former Soviet Union did not prevent a nuclear Armageddon by engaging in an arms race against the United States. It is my belief that the United States would not have abused its nuclear power, regardless of the Soviet Union's nuclear capacity, and so the arms race was not effective. On the contrary, it drew the world closer to a nuclear Armageddon by increasing the number of nuclear weapons in the world, and increasing the possibility of an accident or attack.
I do not believe the Soviet Union prevented a nuclear Armageddon with the arms race against the United States. I believe the Cold War was the closest the world has come to experiencing this problem and neither country is responsible for avoiding it other than not actually using the weapons that were being developed.
In the Bay of Pigs incident, negotiations with Kruschev were close, but good. It was Kennedy who lead the way to peace and safety, or more likely, his cabinet. This is important to know. It seems that both sides were exercising military might and prowess, but from what i've read, the US lead.