No, you could not convert your way to safety as a Jew. It didn't matter if you converted, you were still a Jew. However, Jews who converted and then became priests or nuns were often left alone, at least initially, as the Nazis and the Vatican had a pact. But eventually the Nazis started going after Jews who had converted and had become priests or nuns (Jews who had converted but not become priests or nuns were persecuted just as Jews who had not converted were). One notorious case was Edith Stein. She was a Jew who converted to Catholicism when she was about 31. By that point she had a doctorate and was teaching at a Catholic school. But after the Nazis came to power, she was fired because she was of Jewish heritage and all such were not allowed to hold a teaching job. She then became a nun. Her order sent her to the Netherlands to live at a convent there, for safety. But the Dutch Bishop's conference put out a statement condemning Nazi racism, and in retaliation the Nazis began arresting priests and nuns of Jewish heritage. She was taken to Auschwitz and killed within the week, as well as her sister, who was also a convert and a nun. She was made a saint by Pope John Paul II, but it stirred up a little controversy as she was considered a martyr who suffered and died due to Catholic opposition to the Nazis, while other saw her as being condemned to death due to her Jewish heritage, not her Catholic faith--she'd been spared from concentration camps due to her Catholic faith, but was then condemned due to her Jewish faith. There are a few other cases that are similar.