I would say he would agree with it.
Have you actually listened to Barton? Or only what progressives say about him?
"Where the preamble declares, that coercion is a departure from the plan of the holy author of our religion, an amendment was proposed by inserting "Jesus Christ," so that it would read "A departure from the plan of Jesus Christ, the holy author of our religion;" the insertion was rejected by the great majority, in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and Mohammedan, the Hindoo and Infidel of every denomination."
-Thomas Jefferson, Autobiography, in reference to the Virginia Act for Religious Freedom