I don't think 10x your immigrant population in 2 years is demographically the same as a natural population growth over 10 years.
They result in 2 very different distributions. One having a very large segment of the population in one specific age category. Which also puts a lot of pressure on systems / infrastructure that is relevant to that category.
...because of immigration? Birth rates have been far below replacement for decades now.
https://en.wikipedia.org/wiki/File:Total_Fertility_Rate_of_C...