Really, one would have to be rather fickle to be offended at such a question. Either a person ignores it and treats the question with disdain, or a person demonstrates superiority in intelligence by demolishing the underlying pretext with a demonstration of wisdom that only the Omniscient would possess.
The big question that is difficult to answer, because of individuality, is what sort of an atheist are we talking about. Some atheists might think that life is futile anyway, commit suicide and let the kid (Kid Page) find out for itself what is like to be a goat in the desert. A goat is a goat after all.
But if you mean that an atheist and a child is in the desert together, the question becomes: What is an atheist doing with a child in a remote desert?
You could ask such a question of a cleric. The cleric could be an atheist. But you would not know this unless the cleric admitted that he was an atheist.
If the atheist is a woman, then the child might be her own child. Could the atheist be the father of the child?
People react differently according to their worldview and how they feel at the time. Emotionally immature people go to pieces and have a hissy fit when having to make a decision under a little bit of pressure. Emotionally mature people demonstrate the character of which they are made. Experience is a great teacher in life; that is, if a person wants to live in the light of the truth.
To be honest, since you asked me the question, I would have to say that I would not know what an atheist would do. Although, just recently I heard a soldier, a war veteran of Iraq and Afghanistan, state that when in the trenches or under attack by enemy fire, his experience was that the atheists within his platoon suddenly become believers in the possibility that God just might exist and began praying.
Some Do, Some Don’t, Many Claim That They Wont, But Then You Know They Will