Ah, apparently not:

Cristero War - Wikipedia, the free encyclopedia

"The end of the Cristero War affected emigration to the United States. "In the aftermath of their defeat, many of the Cristeros — by some estimates as much as 5 percent of Mexico's population — fled to the U.S. Many of them made their way to Los Angeles, where they found a protector in John Joseph Cantwell, the bishop of what was then the Los Angeles-San Diego diocese."Under Archbishop Cantwell's sponsorship the Cristero refugees became a substantial community in Los Angeles, in 1934 staging a parade some 40,000 strong through the city."