Well there's a reason that Romney lost to Obama in Florida in 2012, and it wasn't the white vote
Yes. His campaign put out Spanish-language ads attempting to link President Obama to Fidel Castro and Hugo Chavez, and those did not work. Romney seemed likely to win Florida before those ads appeared.
The "Cuban" population isn't so monolithic as it once was. It used to be one of the strongest constituencies of Republican voters when Cuban-Americans were middle-class and upper-class, largely and usually unambiguously white, political refugees from Fidel Castro. Over fifty years there are shifts in such a population as occupational group or level of education becomes more important than ethnic identity. But as significantly, the Cubans entering America during the Mariel boat lift are more working class and less decidedly white. Such makes a huge difference.
Many of the Hispanics in Florida are not Cuban-Americans. People from Central and South America, Mexican-Americans, and Puerto Ricans don't spend their thoughts on such a concept as
iJ--- Castro! (the Spanish word here depicted in this sentence translates as a four-letter word that begins with an F in English).
But in any large state, let us say Ohio or Pennsylvania, even a small Hispanic population could be the difference between a D win and an R win.