No. Survival is our strongest instinct. Besides, human population will plateau around 10 billion or so, and we're already seeing trends, from very early ones to pretty advanced ones (Japan), where people decide not to have kids anymore in modern societies, or even have sex with other humans.

You're thinking immortality would be a problem given the current conditions. But the conditions will be different in the future. The same will be true for food production, which should be vastly more efficient in the future, and enough to feed everyone.