There may be several reasons for the author leaving the narrative to discuss the war as Gene later experienced it. First of all, Knowles reminds his reader that the story is told in retrospect. In the first chapter we learn that Gene is returning to Devon as an adult, trying to make sense of what happened there. So reference to future events would not be inappropriate.
Secondly, the mention of war serves to connect World War II with the events that happened at Devon. We see how flawed individuals are, how easily we are tempted to turn on one another as Gene's jealousy toward Finny caused him to jounce the limb of the tree. But we also see see that we all fight our own private wars, needlessly, against enemies that are not truly our enemies. As Gene confesses,
I never killed anybody and I never developed an intense level of hatred for the enemy. Because my war ended before I ever put on a uniform; I was on active duty all my time at school; I killed my enemy there.
Gene's true enemy was not the Japanese or the Germans, or even Finny. His true enemy was himself and his own jealously and insecurity. This realization causes him to obtain his "separate peace." In this way, we see that Finny, even though he died, had a lasting effect on Gene and that the events at Devon serve as microcosm for the bigger war that was raging on the outside. The enemy may not be who we perceive it to be. It may be, as Gene discovered, ourselves.