Not the grandparent, but I'll add some points anyway:
Replacing large parts of a country's population, culture and traditions won't be possible without 1) societal changes affecting the existing population and 2) societal changes affecting the migrant population. In the end, neither the existing population nor the migrant population are likely to be happy about the end result.
1) Being a part of a cultural minority is a very different experience from being a part of the majority population, and the experience of simply having one's expected but unborn children/siblings replaced as suggested, would, to put it plainly, fuck with a lot of peoples' minds by messing with peoples' sense of belonging, identity, and general trust of society. In other words, if societal cohesion is a priority then replacing the populace will be tricky; many countries have raging debate about immigrants despite having an immigrant population of less than 5%. Imagine the debates if that number was steadily increasing and approaching 50%. My guess is it won't be pretty.
2) Whenever this topic is brought up, the main issue is usually that modern society needs to import workers in order to fill the positions open at the bottom; the existing populace is progressing upwards, since employees are scarcer and wages go up; while the low-paying jobs get filled by immigrants. The problem is that the migrant populace probably aren't really aiming for those jobs; moving halfway across the World to clean toilets simply isn't what most people want, and since linguistical, educational and cultural differences will shut the doors for more than a generation (assuming we don't get _much_ better at integrating migrants into our societies), migration won't provide what many migrants are looking for.
It is definitely possible to compensate for falling birth-rates by the means of immigration. It just won't be a drop-in replacement and it won't be easy. In the end, especially considering other issues, I'd say it's time to have a look at having a look at how to structure our societies in order to manage declining birth rates over an extended period of time. Migration is not inherently bad, and cultures can and will continue to evolve, but importing people to handle the shittiest of jobs available simply isn't a good way of welcoming anyone into your own society.