6K Man
Bureaucrat
A resource tile has 3 principal benefits:
the tile output - e.g. a Horse tile provides hammers and 1 commerce (I think). If the tile is not within the fat cross of any city, this benefit is unavailable.
the strategic use and trading use - e.g. Stone boosts construction of many things, Silver boosts happiness by +1, Copper lets you build Axemen among other things. So long as the resource is in your culture and connected (via the appropriate improvement/fort, road or river), you get the strategic use and can trade it, whether it is in the fat cross or not.
the tile output - e.g. a Horse tile provides hammers and 1 commerce (I think). If the tile is not within the fat cross of any city, this benefit is unavailable.
the strategic use and trading use - e.g. Stone boosts construction of many things, Silver boosts happiness by +1, Copper lets you build Axemen among other things. So long as the resource is in your culture and connected (via the appropriate improvement/fort, road or river), you get the strategic use and can trade it, whether it is in the fat cross or not.