That's a very Berlin-centric observation. Berlin is special; it's hard to extrapolate to the rest of the country.
Anyway, like I said there is a good chance I am wrong about it Germany in general. But I'd argue that in Berlin that is pretty much the case, regardless of how large the "transient" people are compared to "longer-term settlers". Once people start having kids they stop hopping around, so I'd guess that the amount of "non-native" children that dominate the schools have immigrant parents who are mostly settled.