[Baalz]

Yes, the path boosts do seem to effect the phantom paths of the slaves. Here's the test I ran:
Sabbath master has fire magic
4 sabbath slaves with no fire magic (phantom +2 fire presumably)
Sabbath master casts reinvigoration so the slaves are at 0 fatigue to start the test.
Master casts summon phoenix power (requires 2f, 20 fatigue).
Slave gains 12 fatigue (not sure exactly how the math here works out)
Master casts incinerate (requires 3f, 20 fatigue)
Slave gains another 12 fatigue.

So, again, I'm not entirely sure how the math works out on that but the slave gained the same fatigue for incinerate as he did for phoenix power.