Not always.
http://seattletimes.nwsource.com/html/localnews/2002103445_presvote29m.html
Plus, the cities are the economic hubs, the suburbs are bedroom communities that depends on access to the cities. The urban areas are the sine qua non of the "ring cities."
You're correct, not always but I'd bet in the majority of cases. Look at Atlanta, St.louis, New Orleans, L.A. and Austin. They are all surrounded by red counties. Those that live in the inner city vote Democrat, those that make it the economic engines of the state live elsewhere and vote more Republican.