Oh I forgot. You only commented on the 2nd Great Awakening. The 1st Great Awakening which I posted twice started in the 1730s and was the key element which caused the Enlightenment movement to be of little effect on colonial America.
Benjamin Franklin, the oldest of our Founders was in his late 20s to early 30s, during the 1730s -- so if any Founder was influenced by that Awakening, it would surely be Franklin.
And yet, Franklin went the other way -- he sponsored Deist Thomas Paine's move to America, was a high official amongst Freemasons, was notably impious and on his death bequeathed money to every church in Philadelphia, including its Synagogue.
Washington and Adams were both born in in 1730s, so it's hard to suppose what influence the Awakening had on them.
Both were considerably more religious than old Franklin, but Adams was Unitarian, and Freemason Washington never expressed an interest in Trinitarian doctrines.
But let me say, if I may, that you seem to have a very different, and more negative, view of the term "Enlightenment" than I do.
In America the sometimes anti-Christian "Enlightenment" was transformed into a tolerance for all religions, as expressed in our First Amendment.
That's why, in my view the term "Enlightenment" expresses the very best in our Founders, not as this thread intends their "Damnable Heresy".