In a word, no. That's the title to a classic article by Douglass Adair, Marvin Harvey. I can access the whole thing at work through a license privilege. So you may not be able to view it unless you want to shell out $9 for it. Virtually all serious Hamilton scholars follow its lead and conclude that although Hamilton may have flirted with Christianity in college, and then embraced it towards the very end of his life after his son was killed in a duel, during the time in which he was politically active founding the nation he was not an orthodox Trinitarian Christian, but something else. That something else could be called theistic rationalist.
What brings this to mind is this post obviously directed at me. The writer believes something Hamilton wrote in Federalist 31 proves him to be a Christian.
The objects of geometrical inquiry are so entirely abstracted from those pursuits which stir up and put in motion the unruly passions of the human heart, that mankind, without difficulty, adopt not only the more simple theorems of the science, but even those abstruse paradoxes which, however they may appear susceptible of demonstration, are at variance with the natural conceptions which the mind, without the aid of philosophy, would be led to entertain upon the subject. The infinite divisibility of matter, or, in other words, the infinite divisibility of a finite thing, extending even to the minutest atom, is a point agreed among geometricians, though not less incomprehensible to common-sense than any of those mysteries in religion, against which the batteries of infidelity have been so industriously leveled. [Emphasis added]
It's funny, I don't see Hamilton using the word "Christian" but "mysteries in religion." The theistic rationalists supported "religion" in general, not the Christian [or "Judeo-Christian"] religion exclusively. When you see the key Founders speaking of "religion" unqualified by the term "Christian," you can either conclude a) that they meant religion in general, (because after all, that's the textual meaning of "religion") or b) that absent further compelling evidence you simply don't know they meant "religion" to mean "Christianity" exclusively.
Part of what made them "infidels" to orthodox Christians was that the theistic rationalists supported a variety of exotic non-Christian religions as "valid" paths to God. As theistic rationalist Ben Franklin put it, expressing his support for the orthodox Christian preaching of his friend George Whitefield, yet at the same time drawing an equivalence between Christianity and Islam:
Both house and ground were vested in trustees, expressly for the use of any preacher of any religious persuasion who might desire to say something to the people at Philadelphia; the design in building not being to accommodate any particular sect, but the inhabitants in general; so that even if the Mufti of Constantinople were to send a missionary to preach Mohammedanism to us, he would find a pulpit at his service.
Regarding the term "infidel," no one from that era thought of himself as one [being labeled such could greatly damages one's reputation, which the Founding Fathers guarded with their lives], and often the term simply meant someone to one's religious left. As such, the theistic rationalists thought atheists who tried to debunk religion entirely or perhaps religionists who didn't believe God was on the side of America in the Revolutionary war to be "infidels." As, again, rationalist Ben Franklin used the term:
To this may be truly added, that serious Religion, under its various Denominations, is not only tolerated, but respected and practised. Atheism is unknown there; Infidelity rare and secret; so that persons may live to a great Age in that Country, without having their Piety shocked by meeting with either an Atheist or an Infidel. And the Divine Being seems to have manifested his Approbation of the mutual Forbearance and Kindness with which the different Sects treat each other, by the remarkable Prosperity with which He has been pleased to favour the whole Country.
Keep in mind that, to the orthodox, Ben Franklin's unitarian rationalist creed was "infidelity," and though not a majority, theological unitarians like Franklin abounded in late 18th Century America, especially in elite, educated Whig circles. Franklin obviously defined "infidelity" different than did the orthodox. Here Washington defines "infidels" as those who disbelieve God favored the Americans in the Revolutionary War:
The hand of Providence has been so conspicuous in all this, that he must be worse than an infidel that lacks faith, and more than wicked, that has not gratitude enough to acknowledge his obligations, but, it will be time enough for me to turn preacher, when my present appointment ceases; and therefore, I shall add no more on the Doctrine of Providence....
Washington's self-serving definition of infidelity by its logic included the many orthodox Christian Tories who remained loyal to Great Britain and British Christians against whom America rebelled. They obviously didn't believe Providence was on America's side.
The orthodox, on the other hand, understood atheism, deism, unitarianism, and universalism to be "infidelity." Here is, for instance, orthodox figure from the Founding era, Bishop Meade on how theological universalism is "infidelity": “I have other reasons for knowing that infidelity, under the specious garb of Universalism, was then finding its way into the pulpit.” And to show how the theistic rationalists had a different understanding of "infidelity," here is George Washington praising that very "infidel" theology as "sound" religion.
It gives me the most sensible pleasure to find, that, in our nation, however different are the sentiments of citizens on religious doctrines, they generally concur in one thing; for their political professions and practices are almost universally friendly to the order and happiness of our civil institutions. I am also happy in finding this disposition particularly evinced by your society.
The "society" in question was a Universalist Church that denied eternal damnation.
To tie things back to Hamilton, there really are no "smoking gun" quotations until the very end of his life when he embraced orthodox Christianity. His systematic usage of generic philosophical terms for God, during the years in which he was active founding the nation, points to his belief in theistic rationalism. For instance when describing what he looked for in a wife, he could have demanded she be a devout Christian (which his wife turned out to be; you never know with whom you actually fall in love), but he didn't. As he put it: "As to religion, a moderate streak will satisfy me. She must believe in god and hate a saint." This is not how an orthodox Christian would talk. And though his "we forgot" and we didn't need to rely on "foreign aid" quotations, regarding why the Constitution doesn't mention God, are, as David Barton would put it, "unconfirmed," he made worse religious wisecracks. In a letter to Anthony Wayne July 6, 1780, Hamilton discusses a military chaplain and notes:
“He is just what I should like for a military parson except that he does not whore or drink. He will fight, and he will not insist upon your going to heaven whether you will or not."
A theist like Ben Franklin could make such a statement; a serious orthodox Christian would not. During the time in which he was active founding the nation, Hamilton supported "religion" and expressed a generic belief in an active God, but offered no evidence of belief in orthodox Trinitarian Christianity. Though there is room for doubt, the preponderance of the evidence shows he believed, like the other key Founders, in what is better called "theistic rationalism" not Christianity.