To be a consistent conservative you most likely do. Somebody who believes that "survival of the fittest' is the only moral law in nature might call himself a conservative and behave in a manner consistent with his belief by being a robber baron like Andrew Carnegie, a criminal of some sort or a nazi (or a cannibal like Jeffrey Dahmer), but the word "conservative" igtself connotes some sort of an effort to preserve the values which have guided human society over the last couple of thousand years, and it's hard to picture an atheist making any sort of a serious effort to do that, as opposed to merely looking out for number one.
Newt Gingrich put it rather succinctly in noting that the question of whether a man views his fellow man as a fellow child of God or as a meat byproduct of stochastic events and processes simply has to effect human relations.
No, but many conservative principles, and many conservative social positions are rooted in Judeo-Christian morality (in this country, anyway).