It can change the POI. For example, if you have too much pitch it is only the top of the pad that is in good contact with your shoulder/pocket. The gun will tend to recoil upward more because the axis of rotation is higher. Properly setting the pitch makes better contact with your shoulder and, all else being equal, should lower your POI a little.
If you shoot like a 19th Century game shooter then pitch is a meaningful dimension affecting POI. If you shoot like a 21st Century target shooter then pitch is meaningless for POI. It CAN affect perceived recoil like Ajax says. Current top line coach/gunfitter stuff says "0" is a good number or maybe a taste down.
I usually buzz off the pitch to an inch down or so but less is def more and lotsa down can beat you to death.