Lord Parkin
aka emperor
Nope, they don't. Just like you don't have to have your second city connected to your capital in a regular game for the free Monument to take effect. 
As far as I recall, all wonder benefits are shared between civs, except for the Oracle (only one free tech) and the Taj Mahal (only one Golden Age, for the building civ). Unless I'm forgetting anything, all other wonder benefits are shared.

As far as I recall, all wonder benefits are shared between civs, except for the Oracle (only one free tech) and the Taj Mahal (only one Golden Age, for the building civ). Unless I'm forgetting anything, all other wonder benefits are shared.