It seems unlikely. It does, indeed, sound like the kind of myth is used to explain why a lot of people would appear to support a terrible dictatorship — as opposed to a more nuanced understanding of what they saw positive about it. It is a way to not acknowledge that a lot of people can get on board with a pretty abhorrent program, if they are convinced it is in their interests.

I don't know the origin of that particular story, but Solzhyenitsyn has a similar account in Gulag Archipelago about the Soviet Union:

Here is one vignette from those years [the early Stalin years] as it actually occurred. A district Party conference was under way in Moscow Province. It was presided over by a new secretary of the District Party Committee, replacing one recently arrested. At the conclusion of the conference, a tribute to Comrade Stalin was called for. Of course, everyone stood up (just as everyone had leaped to his feet during the conference at every mention of his name). The small hall echoed with "stormy applause, rising to an ovation." For three minutes, four minutes, five minutes, the "stormy applause, rising to an ovation," continued. But palms were getting sore and raised arms were already aching. And the older people were panting from exhaustion. It was becoming insufferably silly even to those who really adored Stalin. However, who would dare be the first to stop? The secretary of the District Party Committee could have done it. He was standing on the platform, and it was he who had just called for the ovation. But he was a newcomer. He had taken the place of a man who'd been arrested. He was afraid! After all, NKVD men were standing in the hall applauding and watching to see who quit first! And in that obscure, small hall, unknown to the Leader, the applause went on — six, seven, eight minutes! They were done for! Their goose was cooked! They couldn't stop now till they collapsed with heart attacks! At the rear of the hall, which was crowded, they could of course cheat a bit, clap less frequently, less vigorously, not so eagerly-but up there with the presidium where everyone could see them? The director of the local paper factory, an independent and strong-minded man, stood with the presidium. Aware of all the falsity and all the impossibility of the situation, he still kept on applauding! Nine minutes! Ten! In anguish he watched the secretary of the District Party Committee, but the latter dared not stop. Insanity! To the last man! With make-believe enthusiasm on their faces, looking at each other with faint hope, the district leaders were just going to go on and on applauding till they fell where they stood, till they were carried out of the hall on stretchers! And even then those who were left would not falter .... Then, after eleven minutes, the director of the paper factory assumed a businesslike expression and sat down in his seat. And, oh, a miracle took place! Where had the universal, uninhibited, indescribable enthusiasm gone? To a man, everyone else stopped dead and sat down. They had been saved! The squirrel had been smart enough to jump off his revolving wheel.

That, however, was how they discovered who the independent people were. And that was how they went about eliminating them. That same night the factory director was arrested. They easily pasted ten years on him on the pretext of something quite different. But after he had signed Form 206, the final document of the interrogation, his interrogator reminded him:

"Don't ever be the first 'to stop applauding!"

(And just what are we supposed to do? How are we supposed to stop?)

Now that's what Darwin's natural selection is. And that's also how to grind people down with stupidity.

(Gulag Archipelago, Harper and Row edition, book 1, page 69-70).

Now I don't know if Solzhyenitsyn actually thinks that happened or not (he credits it to something someone told him, but note the lack of specifics). It has the feel of an elaborate dark joke (carrying out clapping people on stretchers). In Stalin's USSR, and to a somewhat lesser degree in Nazi Germany, there were certainly requirements on enthusiasm and loyalty, and being seen as deficient in these qualities could make one a target. But the idea of a Gestapo, or an NKVD, that is hawkishly waiting to see who stopped clapping first... it is, at best, a mockery of the kinds of surveillance and scrutiny that existed in these states.