If we look at this question solely from the standpoint of ideas and of intelligence, Alexander Hamilton would likely have made a very good president. If, however, we look at it from the standpoint of personality and politics, he would not have.
Alexander Hamilton was a brilliant man. He wrote most of the essays that became the Federalist Papers. He was the one who devised the economic plan that became the basis for the economic development of the United States in the early years after the ratification of the Constitution. He was a very smart man who had lots of good ideas.
However, that is not all there is to being a president. Hamilton was also very difficult to like. He was seen as a very arrogant man who rubbed many the wrong way. He was blunt and very good at making people dislike him. Between this and his contempt for the common people (he favored a monarchy of sorts), he would not have made a good president for the early United States.