The ball has already started rolling, all these countries are seeing stagnating and falling housing markets.

Immigration will maybe be the difference between a large and a small fall, or a small fall and stagnation, but even stagnation is a fall in real terms and just because immigration is happening, it won't protect house prices when the larger trend is rising interest making houses less affordable.

Not only will immigration have to beat death when it comes to housing demand (and I bet on death winning over the next 20 years just because of the size of the boomer generation), but different immigrants have different needs. Unless every immigrant is a high earner or has independent wealth, I can't see them propping up a market which is unaffordable for the majority of people.