To your point about phase-shifting though, I think that's a definite possibility, but relies on preferences of each community, and how they change by generation.

Urbanization is not solely driven by immigrants, but how likely are immigrants to move into lower density housing when they have kids? What about their kids? And their kids, etc? And compare that to non-immigrant (or non-recently immigrated) preferences.

The relative productivity of babies and immigrants is not of interest to me in talking about housing preference, but you're correct that babies don't directly add much to GDP for the first two decades.