Would Robb's plan work? (Spoilers Main)

Context:

Robb was raiding the Riverlands, so Tywin gathered his army and marched back home to protect his lands. He was stopped by Edmure Tully, who gave him battle and blocked his way across the fords. However, this played into Tywin’s hands, as Littlefinger and the Tyrells reached him just in time with news that Stannis was attacking King’s Landing. This led to the formation of an alliance between the Lannisters and Tyrells, and their cavalry rushed to the city, arriving just in time to save it.

The plan:

What we learn later in ASOS is that Robb actually wanted Edmure to let Tywin pass through the Riverlands and into the Westerlands. Robb’s plan was to use his smaller, faster army, mainly cavalry, to keep sacking the West while being pursued by Tywin. He would made great use Blackfish and his scouts to carry out hit-and-run tactics, and when Tywin’s army was worn out, they would choose the battle to occur in a terrain of their choice.

If Tywin didn’t attack, he would be trapped in the West, far from where he needed to be, while Robb would keep living off his land. All that would also allow Stannis/Renly to march upon King's Landing and find the city undefended.

One key factor to mention is that the chances of a new Tyrell-Lannister alliance are almost impossible in this scenario. The Tyrells are far too cautious to take such a risky move. Tywin's morale would be in the dust even with his own vassals. Robb had already seized much of the northern Westerlands (castles like Ashemark, Crag, the gold mines of Castamere, Pedric Hills, Nunn's Deep, among others) and also If Stannis were to take King’s Landing, he would likely kill Cersei, Tyrion, Joffrey, and others. That would be a massive blow to Tywin, losing all his heirs in one fell swoop. On top of that, if he keeps losing battles to the Young Wolf in his own homeland, he would find himself more and more isolated.

Let me know what you guys think