The accent would give them away, but the betters such as her would have been spared and integrated, for nearly 50 years at this point. The refugees who you propose will do the operation would almost certainly be mestizos who would be found out in a split-second by any better with a gun and a functioning eye.
I doubt white-passing Mexicans would have been spared, the RU conception of inferiors seems as religious as it is racial. So they likely wouldn’t spare anyone already in Mexico they found white-passing or not because in their eyes they are Infee Papists.
And I’m sure some white-passing Mexicans would flee rather than submit even in that situation.