I would say no, considering that cut out the miracle parts of his Bible, leaving only the parts where Jesus preached peace and caring for the poor. He also read the Quran. He also exceeded the authority given to the President under the Constitution through the Louisiana Purchase. The standard Republican view of the Constitution is that the government only has the powers explicitly stated in the Constitution. This would be especially problematic for Jefferson because he originally supported this view. Finally, he supported small-scale economics does not jive well with either major party.