In Que Qiao (or whatever it winds up called if the name is random) where Failsafe attacks Morningstar and Lilith it's not only possible, but relatively easy to kill Failsafe if the system geometry puts the gates far enough apart. Once driven off, Morningstar does nothing except fly gatewards and fire its turrets at things in their arcs. If you have a level appropriate weapon with more range than it and a ship faster than it (the Raijin certainly qualifies and the margin is enough that I think the Spartan would as well) you can chase after it and kill it with ease.
This is a natural thing to do if you can and it seems like something the mission structure should try to accomodate, even if just to have Morningstar warn that it relayed warning to a distant drone instead of that it's carrying warning to Luminous if it died.