Yes, a Mormon can win support from evangelicals and other Christians in a run for major office. I know. I’ve done it.
As a member of the Church of Jesus Christ of Latter-day Saints (nicknamed “Mormons” or “LDS”), I served 25 years in elective office–14 of them as a U.S. Congressman–in Oklahoma, a Bible Belt state.
Evangelical Protestants form a majority of Oklahoma’s population–double the national average–and tied with Arkansas for the largest percentage of any state, as reported by the Pew Forum on Religion. Mormons in Oklahoma are less than one-half of one percent.