As far as we know, yes. We have no primary sources for this: Ossip Bernstein himself did not write his memoirs, but we do have two reliable secondary sources in former World Champion Edward Lasker and American Grandmaster Arthur Denker, both friends of Bernstein. Here's an excerpt from page 182 of Denker's book:

"This arrest," wrote Ossip's good friend Edward Lasker, "took place during the 'Red terror,' when the mere fact that a man was a member of the well-to-do bourgeoisie stamped him as a criminal. Bernstein's crime was his role as legal adviser to bankers, industrialists and trusts. There was, of course, no court trial. One of those sadistic minor officials, who always show up on the wake of revolutions when executions are the order of the day, had a firing squad line up Bernstein and a number of other prisoners against a wall. Then, fortunately, a superior officer appeared who asked to see the list of the prisoners' names. Discovering on it the name, Ossip Bernstein, he asked him whether he was the famous chess master. Not satisfied with Bernstein's affirmative reply, he made him play a game with him; and, when Bernstein won in short order, he had him and the others led back to prison and later released."

Yes, I know-yet another story about a last-minute reprieve from the firing squad. But Bernstein was absolutely convincing when he described at length how his hands were shaking when playing against the officer, and I believed his story then and believe it still.

There is an interesting parallel with Alekhine: Both Bernstein and Alekhine were lawyers, grandmasters, and members of the bourgeoisie. Both emigrated to Paris, having claimed a brush with death before escaping the Russian Revolution. It could be that one or both embellished their story, but there's no evidence to refute their account.

Source:

Denker, Arnold S., and Larry Parr. The Bobby Fischer I Knew and Other Stories. Great Chess Literature Series. San Francisco: Hypermodern Press, 1995.