From my experience... Extreme pull hitters with power will hit more HRs. It makes sense because they are dealing with shorter LF and RF fences, than those who hit the ball up the middle a lot.
Now the rest of this is not an exact science but I have seen a handful of hitters where it was the only thing that could explain their production:
Exteme push RH hitters who have a push/pull of 75+ tend to hit higher than they should against their RH counterparts. For instance, say a guy is a RH batter with a RH split of 60. Say his contact and power are both 60 as well. He looks like a .250ish hitter with limited pop. But for some damn reason I have seen guys like this excel if their push/pull is extreme (either way). This guy might hit .285 againt righties and you have no other way to explain it, other than he is shooting the ball to RF (where defense tends to be poor) or between 2B and 1B, which is usually much easier than shooting the ball between SS and 3B (where the defensive ratings tend to be better).
Guys with a mid range push/pull of 49-51 tend to hit higher than they should, no matter what. It makes sense. If a guy continually hits the ball up the middle...pitcher's are normally poor defenders and only the best 2B/SS defenders can rob a hit up the middle. I played a little slow pitch softball in my day and hitting middle was always where games were won. CFs have more ground to cover so they may be sitting 350 feet deep at the time of the pitch. In RF and LF they may be playing 300 feet deep. Hitting middle works in real life and I have seen players that can only have their production explained by a 50 push/pull. Their ratings look average across the board... like 60/60/60/60/60 and for some reason a guy who looks like he should hit .250, is again hitting .285 consistently.
I can't back any of that up by studies because I just don't have the time, but I have seen enough "unexplainable" guys to make me feel like there is something to this.
I have also found that extreme pull hitters WITH POWER (15 or less push/pull) aren't effected as much by splits either. If they have 90 power and a push/pull of 7 (for example) it doesn't seem to matter that much that they have a 47 split against RH pitchers. They still seem to hit a ton of balls over the fence against those righties.
I think where this becomes most useful is in free agency. You have to take the ballpark into effect for sure, but occasionally you will find that guy who consistently hit .250 in Burlington and he looks like he would be lucky to hit .250 in any park. If you look deeper you will normally find one of two things are the reason...speed or push/pull. And it might make you take the gamble on a player that no one else wants, because his core hitting stats look average at best. Take that .250 Burlington hitter and put him in an average park and he hits .285.
Anyway, I'm done. Disregard all of it. I changed my mind. It's all cosmetic. Push pull doesn't matter. ;-)