Can't speak for PQ2, but judging by the original PQ and the little I've seen of PQ2, there will be at least a few spoilers, but the game will try to shy away from anything major if it can. As Micah said, it's at the point where each team is complete, so it's inevitable that you'll come across certain spoilers for characters, including team makeup and details of certain characters (Naoto is the biggest offender if you haven't been spoiled on them yet).
tl;dr don't expect any game-ruining spoilers, but do be aware that the game will reference spoilery details from time to time.