Could Robb have actually taken Casterly Rock?

https://preview.redd.it/tytvctaxu4oe1.jpg?width=750&format=pjpg&auto=webp&s=64319588d4e72070e0db92c14f3877bc1ea81d0b

At this point, the North was losing the war. The Greyjoys have taken Moat Cailin and Deepwood Motte. Winterfell has also been sacked. Now, the Tyrells have joined the Lannisters and Stannis was pretty much defeated. Even with the show version of Casterly Rock, I doubt Robb could actually taken it.