Look at it another way, yes. With fewer people having children, there is less chance of reincarnation. So we can say: if there are no newborns in the world, there will be no reincarnation, that is, no reincarnation without children.
For individuals, there may well be no such restriction. For example, who would stop people who die before they grow up from being reincarnated? Besides, people who don't like children, they shouldn't have children.