Independent North/Vale/Ironlands. Rhaegar lives/loses-Robert Dies/Wins

Somehow in the Battle of the Trident Rhaegar manages to kill Robert (with the power of plot armor), but this doesn't change the aftermath of the battle, the Rebels still win. The battle lasts longer and both sides take more casualties, but Rhaegar retreats.

Tywin Lannister, seeing that Robert died choses to side with Rhaegar.

The Riverlands (more like the Tully's) seeing that now they've got no chance of winning, withdraw from the war effort, leaving the North and the Vale alone in rebellion.

The North and the Vale retreat into their respective Kingdoms, still in Rebellion.

The question I want to ask here is this. Can the North and the Vale (maybe the Iron Islands, if they think they can get away with it and ally with the North) manage to, if not win, but hold out against the rest of the Kingdoms?

Keep in mind this is basically the North, the Vale and the Iron Islands against a kingdom which still has Aerys the Mad as King, and the Prince who had just ran away with a betrothed girl. A girl who is now dead and has birthed the Prince a son.