In a word, no. The State needs the Church.
We have no government armed with power capable of contending with human passions unbridled by morality and religion. Avarice, ambition, revenge, or gallantry, would break the strongest cords of our Constitution as a whale goes through a net. Our Constitution was made only for a religious and moral people. It is wholly inadequate for the government of any other. -John Adams
"Separation of Church and State" was intended to convey that the State should be kept out of the doings of the Church. However, it was inconceivable at the time that it would have been reversed as it has. It was clear from the statements of the founding fathers that virtue (yes, Christian virtue) was absolutely vital to the success of the republic.
A republic, once equally poised must either preserve its virtue or lose its liberty. -John Witherspoon
What then of Christians in politics? I believe that it is wholly necessary. As Christians we should therefore be concerned with voting for those who seem to pose little threat to our freedoms as Christians as well as the objective morality we uphold. Often this seems like choosing the lesser of a few evils, especially when it comes to keeping certain value-deprived belief systems out of office. Being politically shrewd is a quality that evades many, but it is nevertheless important.
On this, see A Christian Manifesto by Francis Schaeffer. It is a short but vital read.