With Castro as Clinton's running mate, she could have flipped at least Arizona and Florida, thus narrowly winning the election with 272 electoral votes over Trump's 266.
Possibly, and in addition, the presence of Paul on the GOP ticket might have wooed just enough libertarian-leaners away from Johnson to throw NH to the GOP-- resulting in a 270-268 win.
I can only imagine the sort of pressure that would have been put on EC electors if the vote were that close.
Paul probably would have been an effective running mate for this very reason.