HC, many of your questions are “just-so” hypotheticals, which seem designed to guide us to a certain conclusion. In this case, it’s that the family prayed, followed by miraculous healing, leading the atheist to turn to God. What choice do we have except to follow your line of thought and agree with you?
That said, with my experience as an atheist, I don’t think that line of thought is necessarily what would actually happen. It’s more like what a religious person thinks an atheist might feel. If this miraculous cure happened to me, for example, it’s not quite as clear that it was prayer doing the healing, as it seems like you think it must be. I would look for evidence in other areas – what medicines or practices were used, and what the effect of my family’s loving attention had on my mental state, for starters.
See, a person’s mental state matters an unbelievable lot when it comes to healing. A strong will to live can make people recover, seemingly miraculously. If they want to chalk that up to “God,” using the religious metaphor to explain and symbolize an actual physiological experience, that’s useful and time-honored shorthand. I can’t fault him for that.
However, atheists are just as different from each other (maybe moreso) than are people of religion. If I phrased your same question in an opposite manner, and asked, “Would the Christian friends of a man turning to Atheism, disown him?” what would you answer? Some Christians would do one thing, some would do another. People are different. And I suspect that atheists, being people, are different, too. ;) Some may well disown him. Some may well not. It depends on their relationship with him, with their own life experience, with their philosophy and expectations, and a million other things – not just their atheism.
Personally, if this happened to a friend, I might think that a positive, hopeful outlook on life changed his health. There doesn’t have to be an actual God for a strong belief in God to change one’s physiology. If he wants to call it God, so be it, and that’s why I have Christian friends. ;)