No, but it will mean they will go older, with less dynamic and more geriatric society, worse economic momentum, and so on.
Historically momentum (not absolute position, which depends on prior trajecory and other accidental factors) is tied to population.
When France ruled the world, it was the most populous nation in Europe (1/3 Europeans was French). When Europe in aggregate was the center of power (through colonialism, science, industry, etc), European countries were in the 10 most populous globally (along with China and India). The decline in influence of Britain, France, etc, followed their population decline - in 1950 still 4 of the top populated countries in the world were European (including Russia) and 8 of the top 20. In 2015 only Russia remains in the top 10, and soon there will be no European country in the top 20.
Similarly, when the US emerged and established itself in the international scene as a strong player and then a dominant one, it also got in the top list of most populous countries.
(Historically, China, with its huge population, was the strongest economy on the planet, until the "historical accident" of the New World in the 16th century. Now that the European momentum has stalled, it's getting back up there again).
There may possibly have been some confounding factors during the twentieth century though, like the hugely destructive war, the shift from empires being a benefit to a cost and their consequent dismantling, and numerous mass casualty and economic disruption events. Russia lost something in the region of sixteen million people to the war.
Also I think you need to be clear on absolute vs relative decline - the population of the UK hasn't declined in absolute numbers, nor has its economy, and whether you mean "size of economy" or "GDP per person".
He's talking relative. And it matters. For example stuff stops being sold/is never sold in relatively small markets. We're starting to see it with China-only products. There are many disadvantages to being a smaller economy, even if in per capita terms things are ok.
And almost all European countries, taken individually, are predicted to fall outside the top 10 by 2050 (moderate chance for 2050 and huge chance for 2100).
South Korea's fertility rate is below 1 and still dropping, for many decades. Many other countries are on a similar path. Has there been any precedent of a country recovering from such deeply negative trend once more land and houses freed up?
If you look at South Korea's population, it's still being going up:
https://en.wikipedia.org/wiki/Demographics_of_South_Korea#/m...
(Edit: Actually in 2020 it went down for the first time in recorded history, it seems)
Give it a few more decades, when people actually start dying off en masse (because we haven't really found a way to reliably have masses of centenaries living), and then you'll should see the population dropping. Unless they increase immigration.
What I'm saying applies once the population actually drops by a large amount.
Oh but this is exactly what I'm trying to explore with the South Korea specific example. By 2100 they are predicted by the UN* to have 1/2 of their current population. This remaining bunch will be mostly very old people, the fertile/working age fraction will be like 20% supporting 80% people too old to work or reproduce. This is already a never seen before situation (in peaceful times, at least), which you describe as "numbers tend to move back up, or at least stabilize", like we've seen this many times before, but we've never seen anything like that. Also, I'm having a very difficult time imagining a half-a-century long, continuing freefall in fertility suddenly reversing in another 5-8 decades and them all of a sudden starting to breed like rabbits in 2100, after they lose half their population. Even just to stop the freefall they would have to double the current fertility rate just to not go completely extinct around year 2150.
* https://www.bbc.com/worklife/article/20191010-south-koreas-p...
When your main home + a vacation home cost half of what your main home would have costed 3 decades ago, and you can afford them when you're 25, that's a huge relief right there.
The big question mark to that is that the entire economy doesn't collapse and also takes down salaries with it. But South Korea is quite export oriented so they're better positioned than some other countries.
Plus, once there's an abundance of things (land, houses/apartments, etc.), numbers tend to move back up, or at least stabilize.