Thomas Kidd, of Baylor University, argues they would have in this op-ed published by USA Today: Founders would agree that "In God We Trust." Kidd has published on Patrick Henry, so much of his argument pertains to the early Republican/Jeffersonian tradition, but the Federalists (like Hamilton and Adams) were equally insistent that Providence governs the affairs of men and that our rights and duties flow from divine wellsprings, rather than the arbitrary diktat of the State. Even the most religiously skeptical among the founding generation -- Franklin and Paine come to mind -- affirmed the existence of Providence and God's superintending care over human life. While the Founders may have had a broad diversity of religious opinion regarding orthodox Christian belief, God as the providential source of human rights was key to the principles of our Revolution and the formation of the early Republic.
[Cross-posted over at American Creation.]