No it won't. All first world countries have less than sustainable population growth as it is. We produce vastly more food than we need, and will be able to produce even more in the future with genetically engineered algae. We have vast areas of the Earth left to settle including deserts, antarctica and the Oceans. Not to mention space. We have millennia worth of nuclear fuel available on Earth, not to mention other forms of energy. Overpopulation is a joke.
The way I see it playing out, if working life extension technology is discovered, it will first be hoarded secretly for many years / possibly generations while the rich + powerful use it to stay in power. It won't be generally accessible until much later, likely after the world is in ruins, if at all. Some people believe that it had been discovered before but lost to the ages. Creepy to think about, but makes sense. If someone could live forever, I would think they'd become a huge target for assassination.
That's a stupid theory. All technologies become available to the general public after a short time. Initially cell phones were expensive, but now even the poor often have iphones. Most medicines including advanced cancer treatments are available to everyone. Especially in countries with socialized healthcare. I see no reason why this would be any different.
In the next few decades maybe. But population growth is a very long term issue. Over the next few centuries we will almost certainly solve or adapt to whatever issues global warming creates in the next few decades. Slightly decreasing or increasing the population will not make much difference.
