well, Robb is married, but John Arryn still gets assassinated?
So Robert would still request Ned be his hand, the court comes to winterfel, Bran sees what he sees and gets pushed out a window, Joffrey still hires that assassin, Jon still goes to the wall taking Tyrion with him, Cat still captures Tyrion, Ned still gets attacked, Cersei still kills Robert, Ned still gets beheaded
I think most things would stay the same except now we don't know who the reach supports. would they still back Renly as the candidate for King or would they back Stannis? Lets say they still back Renly and Robb is still called the king in the north, Then stannis still assassinates Renly, but instead of the reach switching their support to the lannisters, they would stay with their ally in the north.
That means when Stannis attacks casterly rock, no last minute intervention by Tywin Lannister, who would be dealing with the combined assaults of the Reach, the riverlands and the north, (which means the Rock will probably fall). So Stannis takes Kings Landing, but then where does that leave the rest of them?