Although the war was initially a local territorial dispute between Peru and Ecuador, it ended relatively quickly with interventions from several countries including the United States. A more secure peace treaty agreement was made (the Brasilia Presidential Act) and diplomacy and democracy prevailed where conflict initially created strife. I do believe this war followed the democratic peace theory.
No, the Cenepa War did not follow the democratic peace theory, because Ecuador initiated the skirmish when they decided that they simply did not like the border treated following the war in 1941. The conflict continued for more than fifty years following Ecuador's actions, and Ecuador's actions did not follow the democratic peace theory because Ecuador affirmatively initiated the conflict.