If Romney were to be president would he have to follow what the church tells him to do?

I have studied the LDS religion. I am not saying its right or wrong... but the way they are structured the members of each Ward have to do as the Bishop calls them to do... and by extension, they have to do what the Prophet of the church tells them to do in the name of the Lord. So if Mitt were to be elected President, would he consult than with the Prophet of the LDS Church since his beliefs would be that Gordan Hinckley has a direct line of communication with God.