No, John Adams did not believe the Constitution applied to some citizens and not others. He was stating his opinion on the character of a people that would be able to live by it.
I did word that badly. Notwithstanding, Adams words with respect to the Constitution being “wholly inadequate to the government of” those people who are not “moral and religious” means that the punishment of such people by this Constitution is to be swift and fair while not draconian—no way does it allow for the peace of the moral and religious to be disturbed as it is today.