No, not really, because Jefferson as mentioned above wasn't a Christian. About half the founders either were not Christian, or were at best "nominal," Christians for public show. Jefferson is clearly not in the Christian camp, in his writings you will see that the Creator is Nature's God, which was Enlightenment code for a contrast to Jacob's God. Nature's God made the laws of the universe and walked away never to be seen or heard from again. He was following in the Greek Natural Law tradition. So it would be a complex statement, but Jefferson would probably have said that nature itself reveals that men are naturally equal and free and that "natural" rights are self evident in the physical nature of being human. As an example, and one quoted by the Massachusetts's Supreme Court in legalizing gay marriage, there is a "natural" right to marry. It is inherent in our species. As such, the state has no authority to determine who can or cannot marry, subject to the state's protective authority to prevent physical harm, such as in a shotgun wedding or to prevent incest or some other form of violence or duress. As such, it is in the nature of our species to pair bond. For other animals, this is not the case and so they would have no "natural right" to be married.
The Massachusetts's Supreme Court went further in pointing out that its constitution is a constitution written during the Revolution and defines state powers very narrowly. All other powers are natural to people. It went on to point out that in statutory law, since the Puritans were anti-Catholic and Catholics said marriage was a religious institution, marriage was defined in Massachusetts as having no religious component being only a secular contract between two people.
I point this out because the early religious thinking doesn't jive in most parts of the United States with modern religious thinking. The civil penalty for failing to attend Church in Massachusetts at the time of the Puritans was to have your tongue nailed to a post for a full day. You would be removed from the post only the next day, after people egged you and so forth. Likewise, prior to the passage of religious freedom, being a Baptist in Virginia was punishable by death. It was Jefferson's work that lead to allowing people to be free from persecution due to their religion. It was his opposition to religion and hence self interest that he propose that autonomy of person, expressed in natural rights like the freedom to choose religion, was our national goal.
That, by the way, is why in the early 19th century you see pro-slavery arguments being ones on the nature of blacks intelligence, skills and so forth. They were naturally inferior and hence had to be protected like children and could not make choices for themselves and so on. It was the argument of the "White Man's Burden." An argument from religion would have fell flat on its face until about the 1920's in the United States and really not until the mid 1980's was religion a credible source of legislative decision making.
So the American Constitution is grounded in a morality driven by science, given the Jeffersonian ideals, and not at all by religion. Jefferson did feel Jesus was an important moral philosopher and put him above or below others in stature depending on the period in his life. His bible as mentioned above removes any miracle related items, or anything that would imply the existence of a god or that Jesus was a god. He felt his followers were frauds and made it up to get followers.