Yes, this can be so. Often at times when there is too much Dukkha, there is not enough time left to think of other things except just the sense of survival. Though with the wish for health, that is an "iffy" one, but certainly for war and cruelty and extreme suffering, certainly if one has better conditions it is often much easier to practice. However, on the other hand, if a person is in such a situation it often will actually bring out, for those who have that potential, some of that courage of the human potential. But for many people, it just encourages fear and the wish for survival.
Certainly I would not wish war, cruelty and these extreme things to be necessary for human beings. It is not part of suitable conditions for developing the Dhamma. Perhaps if a person is more developed, they may be able to go into these situations with much more balance and power, but usually there is just too much Dukkha.
Now, the wish for health, from some of the stories I have heard about people developing, when they actually realize that they are vulnerable in these areas, sometimes it can help a person to turn to spirituality. So, it depends on the degree to which the person is diseased or in ill health because sometimes with Dukkha, if you know Dukkha, you will often seek the way out of it. But in all cases I would certainly wish for the mental capacity to deal with whatever Dukkha is arising in the person's life.