Well, I just checked my facts. Actually, it's nowhere mentioned that PCS affect your army leading modifiers. Neither in wiki or in game. What is mentioned everywhere is that your martial skill affect those modifiers.
But since Holy Fury came out I noticed that a higher PCS meant far more efficience in battle leading. Anyway, this may be based on the fact that higher PCS usually mean higher martial score. But I'm pretty sure leading traits weren't so efficient combined to martial before Holy Fury.
Anyway, I'm still pretty sure that putting a character with five in martial, 60 in PCS and organizer increases movement speed more than a character with 10 in martial, 5 in PCS and organizer. And the reason why I think this is that in my current zunist run finding excellent commanders was really hard in the very beggining and I took a lot of characters with lame martial scores but pretty good PCS and they were doing great at increasing army speed and besieging according to their leading traits. They outrun abbassid armies with good martial commanders and traits that increase army speed. So maybe there's something I'm not seeing and PCS really doesn't affect army leading modifiers. But this is really doubtful imo.
As said, I won some desperate battles against huge armies with better quality than my troops, my martial wasn't this high (well, it was 20 something probably so still good

) but I had terrible PCS and other commanders too.
I need to do some testing, but whether I'm right or wrong on the PCS affecting combat modifiers, I'm absolutely certain that very high PCS even with no leading traits is just a guarantee to win most desperated battles.