I think House Stark is out of the picture at this point in terms of political power and influence. Winterfell has been destroyed, Eddard and Catelyn and Robb are dead and the remaining children are scattered and missing or believed dead. I would imagine that Tywin's first order of business will be to promote somebody and grant them title and land in the north, just like he gave Harrenhal to Littlefinger after Blackwater. You wipe out your enemies and repay your allies with positions of power and influence in previously contested areas. Occupying the north with Lannister forces and allies will kill whatever might be left of the rebellion. The north is really up for grabs at this point, and I don't think Tywin is the type to ignore that for very long.
Politically, I don't think it matters any more whether or not the Stark kids are out there, because the house is so shattered that nobody is going to give their allegiance at this point. It wouldn't surprise me if Tyrion gets sent there with Sansa, as there were hints that Tywin would give him an appropriate home at some point. That would put a Lannister in the north along with a surviving Stark, which just might be enough to satisfy any of the northerners who still have some loyalty to the Stark name.
Tywin really knows what he's doing.
