No, you can't just "build more apartments". For these new inhabitants you will need more grocery stores, more bus/subway stops and overall transportation, more hospitals, more firefighters, more restaurants, more gyms, more tennis courts, more of everything.
Of course. Big cities with all this infrastructure are nothing new. They existed in the past and are big in alive in Asia and other parts of the world. Only in North America we have this bizarre world where it seems like a strange thing to build cities and provide infrastructure for workers!