Are you kidding me??? Would give them away to whom?? Maybe to other Mexicans, but not to our Border Patrol. There's a difference in the way people in Minnesota speak vs. people in Texas vs. people in South Carolina vs. people in Boston, vs. people in Oregon.... You think anyone who isn't a native English-speaking person could tell the difference?? Our border patrol (or 99% of them) won't be able to tell the difference in Spanish dialects.
And you know this how?
I'll say it again. Put a native born Texan on the Texas border and he'll know the difference in the first sentence. Send a BP from Minnesota down and you've got trouble.
A very high percentage of Border Patrol agents, at least along the Mexican border, are hispanic themselves. They could "hear" the difference. Heck I can (or could) hear the difference between northern and southern Mexican accents, and even more easilty between them and Cuban (my spanish prof was Cuban). I can, or could, also tell when someone had an accent that I did not know the origin of. Even when I haven't a clue what they are talking about, that is when I can't understand most of the words, since my Spanish vocubulary is about on the level of an 18 month old native speaker.