One, it wouldn't be fair to the other player (credit to the above answer), and two, you should piece together, with a friend you get NO experience in any battles.
It's pretty much the same as the first answer, you're not being fair boosting you're power, and you get NOTHING from the battles.
So no you can't.
Because if you were to level up in battle it wouldn't be fair to the other player. And no you cannot earn EVs during battles. (Hope This Helps!) :)