There are definitely Talmudic sources about non-Jewish persecution causing the Jews to do teshuva. (A famous quote from the Talmud is that "King Achashverosh handing his signet ring to Haman did more to make the Jews repent than all the preaching of the prophets...")
Similarly, Rabbi Chaim of Volozhin (early 1800s) has the noted saying that "either the Jews make themselves special in a good way, or the non-Jews single them out in a bad way." ("Either we make kiddush, or they make havdalah.)
That's really all I can think of (and I'm not bothering to see the video you've linked): in a cosmic sense, some good may come out of persecution, as it reminds Jews who they are.
But for a well-meaning non-Jew asking what they can do to help? Please don't persecute us, thanks. "Oh I'll just go knocking on the doors of lapsed Jews and telling them to identify more!" Again ... no thanks.
The Talmud says (to paraphrase slightly) that "converts are a big headache for the Jewish mainstream"; one interpretation is that their religious sincerity puts the "blue-blooded" Jews to shame. If that's how we view converts, I'd have a very -- very -- hard time swallowing a notion that non-Jews should be knocking on my door and telling me to be a better Jew.