He's not happy about illegal immigration and the crimes that have come with it. Arizona has been hit pretty hard. We shall see, as they say.
I agree with half of your assessment. IME, legal immigrants are probably the most cohesive opponents, as a group, against illegal immigrants. If you have a strong platform dealing with illegal immigration, then you are probably going to get strong support from naturalized citizens (and green card holders voting in local elections.)
as to crime, though: it's an irrational argument. Illegal immigrants commit far, far, far less crimes
per capita than do natural citizens in the US, and it isn't even close. Just think about it rationally: why would such an individual willfully, and even accidentally, bring such attention to themselves and thus their status? They tend to be the most "law abiding" citizens (outside of the immigration part, obviously--lol), and tend to pay more actual taxes into the system than individuals like Trump, who actually bleed the system dry to benefit their largely criminal enterprises.