No.
You obviously can't distinguish citizenship by race. Also, it's pretty evident when they don't have identification when they get confronted by cops, people run. Also the people who support nativism are real ignorant, really it stems from an overall bigotry of foreigners.
If I remember correctly most of the immigrants leaving are from Indian communities (like Oaxaca) and even Central American countries like Guatemala, which are really poor and have bad living conditions. I would think most of them would speak Quechua or another native dialect, rather than Spanish as many people would assume. Spanish and native dialects have very little similarities, which is how middle-men on the boarder can take advantage of them just for their money.
They either get lucky or they end up one of the nameless dead that have died trying to get to America. It's really distressing to read about. PBS did a documentary on a population of immigrants in Long Island, it was titled "Farmingville". I suggest you watch it and come to a conclusion.