The manual says that if neither side gets an Automatic Victory based on National Morale then "The side with more VP's wins the war and the level of victory is based on the VP difference."
As far as I can tell Victory Point are not used to determine anything about Victory or its Level. For example I played out the full campaign scenario as the CSA player all the way to Early January 1866 (Turn 115). The Morale Points were 90 CSA and 98 USA. The Victory Points were 4512 CSA and 6056 USA.
The game on the last turn declared the war a "Stalemate".
Is there any other result possible due to VP levels?