I doubt you would greet the President in the same manner that you greet a person in shul. You would not say hi in an offhanded manner to him.
That’s only because I don’t have that degree of familiarity with the President. I wouldn’t give an offhand “hi” to a total stranger either.
I would, however, greet the President with the same “Good Morning, sir” that I would give to any other person whom I don’t know (and yes, I often do use “Sir” when greeting and thanking people.)
The Wolf