No, by and large, the founders were not Deists in their religion. They were distinctly Christian, though perhaps of a certain type of prayerful and awe-struck faith which is unrecognizable to much of our current shallow religiosity. Regardless of how they are regarded by modern historians, these were men who held the firm belief that what was happening on the American soil was directed by the Divine, and saw it as the outworking of his desire for freedom.
Thus, they famously penned:
"When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation."
And so the Declaration of Independence begins, looking up to the Divine Giver of Life for the source and sustenance of liberty. This liberty, however, is not bound to political ideology, but rather encompasses the entirety of a person's being. It is not simply the absence of conflict, but the reigning presence of peace. These objectives cannot be wholly accomplished without Sovereign intervention, and these founders had such a concept at their very core.
The course of human events implies a purpose and a reason for the activities under heaven. Far from implying Deism, this echoes the words of Qoheleth and asserts the universal Lordship of Christ, which has accomplished such an expanse of freedom. It appears that this particular course of human events still resonates today, for we live in a world which has greatly benefited from the faithful commitment of these Founding Fathers - such that we have seen more progress and accomplishment in every aspect of life in these past 234 years than the world witnessed in the previous 5000 of human record.
We do not affirm any sort of exceptionalism that says one nation or society is more special to God than another, or that he has somehow chosen one nation to lead the world to heaven. Rather, we affirm an American exceptionalism that says any society which is founded upon and retains those truths which are self-evident and endowed by their Creator is a nation that is blessed. In other words, if we live by his precepts we will reap his blessing - this is biblical and foundational . . . but sadly lost on many.
The course of human events marches on under the watchful eye of its Sovereign.