Suppose the Arryns declare for Robb at the outset; maybe someone gets a hold of the reins of power and honors bonds of marriage and friendship. Does the Stark/Tully/Arryn alliance have the numerical superiority to quickly take out Tywin, gven Robb’s seeming invincibility on the field? I figure if the Lannister forces are beaten quickly, Joffery loses his throne no matter what, since Stannis marches regardless.

I think so, yes. Between Robb’s army, Edmure’s army, and Roose’s army, you’ve already got 27,000 men to Tywin’s ~20k. Add the 30,000 knights of the Vale, and Tywin’s not only outnumbered by more than two to one, but you’ve got enough men to successfully put Harrenhal under siege. 

Indeed, depending on how early the Arryns mobilize, it’s possible Tywin gets trapped north of the Ruby Ford and never even makes it to Harrenhal.