As long as the CnC is active, you will get his bonus for all Generals in his Theater (including other 3-star Generals, I believe). Remember that there are also Sea Theaters, but unfortunately the filter does not show them. To learn about the Sea Theaters go to the folders of the game \GameData\Areas and read them in the various region clusters.
The CnC's importance depends on his basic stats and acquired specialty. When you have the opportunity, try to have your best "Strategy" General win battles and gain promotions, as to become the highest in the hierarchy. A high "Strategy" attribute (4+) means that this CnC is more often active than not, giving his bonus to the rest of the Generals.
Regarding the CnC "specialties", these depend on the historical attributes of the Generals/Admirals in question, mostly, but I have found that a "Genius" General has one of the best attributes. Moltke the Elder is one of those and combined with his surreal high Strategic skill he is unstoppable as CnC. Of course other specialties might provide different attributes, ideal for different theaters (ie in a mountainous theater a CnC specialty that increases the combat width or adds to the initiative/defense is ideal).
Read about these in \GameData\Abilities, mostly between 363 and 418 (and I think incidentally they are in order of importance for Army and Navy). For our our sake, Nature has not allowed another "Napoleon" or "Wellington" (the absolute Army Generals) or "Nelson" (the absolute Navy Admiral) to appear.
