Though I agree functional immortality would probably lead to ugliness whether it was widely distributed or not. The population spike alone would wreak havoc.
Depends on a number of factors. Now if it was wave a magic wand and everyone instantly becomes immortal and the elderly become physically young enough to become physically active and productive members of society who are also able to have children once more virtually overnight. Then yes, we'd have problems.
The most likely progression is we're going to initially find ways to extend life expectancies by up __% with the longer term of the exposure, the greater the life extension. Metformin, a drug often used for type 2 diabetes since the 1950's in some countries, has shown traits not much unlike that in lab studies with mice, where mice treated with it from birth enjoy 150% of the life expectancy of the control group. (Diabetics on it haven't seen anything that extreme, but it is now getting a study done on it, specifically for longevity impacts because of related earlier findings. The diabetics on metformin instead were simply living slightly longer than their (healthier) peers were, even though they often were suffering from a wide array of other health ailments that should have caused them to die earlier, not later)
So if lab studies carried over to humans, it is possible if someone started dosing their toddler with Metformin, and that child continued taking it throughout their life, they could live to see their 140's assuming they don't pick up any other bad health habits or problems along the way. But giving it to someone who is 50 years old on the other hand, he's probably not going to see a very significant improvement, maybe a couple years, possibly even an extra decade depending on numerous factors, but then again maybe not.
However, that does play back into some of the people out there saying the first 1,000 year old human (in non-biblical record keeping) may very well be alive today, it just a question of if they were born this year, 5 years ago, or if they're possibly even older. Because we've only just now begun to seriously acknowledge it is possible to do it. But if current drugs being researched give humans the theoretical ability to live to 130, what are we going to have in another 20 years? 40 years? Or in the case of that theoretical 1 year old put on metformin, what medical tech for longevity/quality of life would be around by the time he turns 100? 125? Even assuming that what they find only works to maximum effect if you start on it while young, it isn't impossible(probable is another matter), that by the time he hit 100, they know enough to keep him kicking until he's 200(and possibly keep his grandchildren around until they're 400), which gives them another 100 years to extend his life even further.
In the meantime everyone else that came before him still dies, they'll just die off at a less significant rate, as the "elixir of long life" simply came along a little too late for them to gain the full benefit. Or even, going by deGray, assuming they can pull the engineer approach and "intervene" in the aging process, and potentially reverse many aspects of it, it will likely be that those treatments come along too late for many or even most people to benefit, as the process itself may potentially kill them due to health issues or advanced age(the irony).
Even then, the 1 year old today is in a much better position than even a High School Student is today on that front. No process is going to be perfect, and the first people pass any given age marker are probably going to end discovering new issues that will in turn need to be addressed(What kind of health issues would a 300 year old human be likely to be concerned about, are there any new ones to be had, or are they same ones a 70 year old often sees today?), and each new issue they hit as things progress is likely to become increasingly more complicated. Even if technical skill, and technical abilities to diagnose and asses the issue continue to increase considerably(aided by long lived researchers), those problems will take time to resolve, which means there will likely be "aging plateaus" along the way.
So yeah, basically, I don't expect death from age-related issues is something that will become an unfamiliar concept to people we deal with in our daily lives anytime within the (potentially greatly extended) lifetime of anyone viewing this forum. Even if someone in here eventually does join the 1,000 year old club.
As to where that population goes, I tend to think Space is very much a significant portion of that answer, and literally puts an entirely different spin on Generation Ships, I think. As you suddenly have crews that could potentially live long enough to reach the destination without getting anywhere close to the speed of light and significant time dilation.
Other economic impacts not considered: Education becomes a more "interesting" thing, as it will then experience something of a paradox, it will slowly become less significant in terms of how much of the economy is engaged in it, as the % of youngsters running around compared to the number of adults that are around shifts considerably towards the adult side. (Although "reproductive longevity" in particular where it concerns women, becomes interesting, I think) While at the same time, education presumably becomes more important in order to function within an increasingly technical society.
Of course, extreme human longevity may have other kinds of fallout for education in general, both good and bad, because it removes a lot of the urgency factors on a number of fields. Hiring to achieve "replacement level" for industries and companies where people work long enough to retire starts to see their bar drop, as fewer people NEED to retire. Training practices and other related things then have a basis for being revisited. Having Grandparents, Great-Grandparents, and Great-*-grandparents around to help raise children, rather than needing help themselves, changes dynamics a bit as well, and can hit education from behind as the *grandparents may be more than happy to help directly assist in the education of their descendants. And people thought homeschooling was getting out of hand already....
