Maybe, but a quick AI-assisted research says that Bremen has an even higher rate of births from non-German mothers than Berlin, and the data does not make the distinction between citizenship and immigration status.
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.