Cuban vote, yes. "Hispanic" vote, certainly not. Nationwide, Cubans make up a very small percentage of "hispanics". Cubans may have tilted Florida to Bush, but that was canceled out by the Mexican vote in NM and other regions throwing their states to GORE. Take out their votes, and Bush probably won NM easily. The "hispanic" vote overall certainly caused Kennedy/Johnson to win the 1960 election. Otherwise, Texas' electoral votes would have ended up in the Nixon column, and with them, the presidency.
And most Cuban Americans are law-abiding folks fleeing persecution in an oppressive, communist country. They're very open about applying for asylum for being political prisoners and don't need to sneak into this country.