So his suggestion of getting a JAA license will not work (assuming there is no JAA flight school in NY near his Uni).
Although I would assume that when the university has an official and published vacation, he would be able to use that vacation to go to another state (FL, most likely) and do flight training.
But I agree that in all respects the primary purpose of the visit to the US (the uni study) has to be maintained as such throughout the process.