The LDS Church argues that the freedoms granted by the Bill of Rights paved the way for the Restoration of the Lord's True Church (which arguably couldn't have happened under other socio-political systems of the time). So, Mormonism is rather intimately linked with the Constitution in that regard. I suppose Faith would likely argue the same thing about her brand of Christianity: the Constitution and the Bill of Rights were necessary steps on the road to the emergence of the True Way.
I don't think Faith would argue that. As I hear her, she believes that people have consistently held the same views as her for the last 2,000 years - the early Christians; various sects deemed as heretics after the Roman church polluted Christ's message, and then some of the non-conformists and Protestant reformers - all forming an unbroken chain to today's True Christians.
I'm sure she can speak for herself, but that's how I saw her views anyway.