So are we assuming that there are a couple instances of hax on each side that could be predicted, or it would be occuring every other turn (still predicted)? Also how would you know when your opponent will get it? Is each player's hax determined by their own RNG's actions?
So, what new game would Pokemon be if both players could predict opportunities of "luck"? Knowing when they'd get a critical hit, knowing when their opponent would get criticals or freezes, etc.
Depending on the answers to the last questions, it would cause chaos I think. Imagine if someone misses their seed. They'd probably just DC, which is already a big enough problem. Also what are we supposed to do, SR and do a bunch of flips before every battle? A WiFi battle takes long enough as-is without increased preparation.
As for the match itself, I think people wouldn't really consider packing a Shell/Battle Armor user (who's to say it would be a good switch-in anyway?), maybe use Honchkrow/Absol a little more, maybe use Sniper Kingdra / Drapion a little more, maybe use + critical hit moves a little more, but things like Feint Scizor are completely inconceivable, IMO. I think teams would remain pretty unchanged for the most part. One think I think that would really change would be that people would hang onto "death fodder" a lot tighter, to absorb the hax with little consequence. Also, if someone is waiting half a battle trying to make sure they get their Sniper Kingdra in at the right time to Draco Meteor the shit out of something, are they really going to play the best match in the meantime? Probably not.
I could be wrong, but I think people would freak out over this for a while, then realize it's really not for anyone's benefit to dedicate time and energy learning and applying this process. I think you'd see a lot of sigs saying "no hax manipulation" next to their battle FCs.
That said, it actually be used in tournament finals or something to prevent hax from occuring, which would be cool, but that all depends on if people think hax is "part of the game" and therefore shouldn't be eliminated.