Depends on what missions we are talking about and depends on what is tried!
Since the upgrade, I have been experimenting with two of our systems. A day or so after the update, we had two systems go into pending then war. One system I completely ignored and that ended in a draw. Second system I foght in CZs and that was won. Three days later both these same two systems went back into a state of war. now we get to answer your question
I ALWAYS monitor traffic and for the duration of these wars there was just me plus another ship that passed through doing our daily tick run.
System One.. MISSIONS only and by missions I confess that all I done were mostly assassinations but I did the occasional Black Box mission, so YES, missions do work but please note I have only done two types of missions.
Oh and the second system I left for three days and then did a number of medium Conflict Zones and that war was won. We need folks to experiment and keeps us all updated but for me the bugs surrounding the Conflict Zones is taking away the enjoyment of playing this excellent game.