“Theoretically he could since he isn’t going to win New York anyway. But there are better choices than Giuliani.”
Not exactly. What the 12th Amendment says is, "The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves..." Under the situation of a Trump/Giuliani ticket then the only electors that would apply to would be New York.
Thats why I knew that Cheney was going to be Bushs Veep when he hopped on a plane to Wyoming a few days before the convention in 2000 - he had been a Texas resident while working for Halliburton, and needed to re-establish his Wyoming residency.
Because there was no way that Bush was going to win without the 32 electoral votes from Texas. And they were right, too.