I was wondering since I've done a speedrun of this game and my friend hasn't, If I'm farther then him in the story it doesn't effect the run right?

coop unlocks when you finish the gcpd but if my friend isn't at that point when I am I would just keep going through the story And he would join when able.

No, both players must complete all missions. I doesn't matter when they join it just matters that they are at the same point in the game as Player 1.