Sophie Chotek was an ultra-Catholic and clericalist, and believed that she had been given some sort of a personal "holy mission" to save the Habsburg dynasty and its empire. Of course, it's hard to say how she would interpret that "holy mission" in the wake of the assassination - a call for peace, or for revenge?
Anyway, she was not liked or respected at court; so whether she comes out in favor of peace or war, it probably wouldn't have made much of a difference. There are only a few who would have seriously listened to her. Still, things could get interesting if she tries to, say, appeal on the Pope to intercede and defuse the situation.
Another question is - if the bullet meant for Potiorek doesn't hit the duchess, does that mean it hits Potiorek instead? That could result in a better Austro-Hungarian performance in Galicia, and avoid their disastrous first offensives against Serbia (with some chance of a more successful later offensive). It might also avoid some of the Austro-Hungarian army's massacres and war crimes on the Balkan front - but only some, as most other Habsburg generals were nearly as bloody-minded as Potiorek. In any case, this would have little to no effect on the war effort itself. Perhaps a less severe famine in Austria-Hungary, but owing more to events in Galicia than to the lower degree of devastation inflicted in Serbia.