Okay so this is what I've heard:"Pokémon can now gain effort values from battling even at Level 100, and stats are recalculated at the end of every battle instead of only after leveling up, much like Deoxys in the Generation III games." But I've also read: "...at level 50 you need 8 EVs to get 1 stat point, meaning 252 EVs will only translate to about 32 extra points in any given stat at level 50."
Which then brings to my actual question: Does that mean that if I had a Lv 50 pokemon with 0 EVs and I fought 63 pokemon with a power bracer without leveling up (though that maybe impossible unless they're 63 lv1s and even then still) I would see my pokemons attack stat increase by 32 points?

You would, but you shouldn't be fighting 63 Pokemon. Power items give +4 EVs in addition to what the Pokemon would have given you.

If you were fighting a Pokemon that gave 1 Attack EV, you'd get 5 EV per battle. Thus you would have 255 EVs since you would have gained 315 EVs from 63 battles but are capped.

If you were fighting a Pokemon that gave 2 Attack EVs, you'd get 6 per battle. Again you'd have 255 since that adds up to 378.

If you were fighting a Pokemon that gave 3 Attack EVs, you'd get 7 per battle. Again you'd have 255 because you'd hit 441.

Now if you were fighting a Pokemon that gave EVs in something other than Attack, your math would be right in that you'd have 252 Attack EVs and 63/126/189 EVs in that other stat.