I doubt the Rock would fall any time soon, but Lannisport certainly would. And while I don’t think the West as a whole could be held long-term, the Ironborn probably could hold onto Fair Isle and the Kayce peninsula for some time.
Now, timing gets important here. If Lannisport falls long enough before Blackwater that the Tyrells hear about it, there’s not going to be a deal with the Tyrells and Tywin will be even more desperate to get across the Red Fork, which might delay him enough so that Blackwater resolves before he can get there.
If it takes longer, then you might see the war pause for a second as both sides recalculate: without the need to retake the North, Robb now has a total fighting strength of 45,000 on the ground and potentially another 17,000 in the North he can bring down. That’s close enough to the Lannister/Tyrells’ 65-70,000 that pulling out of the Riverlands isn’t necessary. If Robb can defeat them in detail or force them into enough defensive battles that he can wear down their numerical advantage, he could win the war.
In addition, with a powerful navy on the west coast, Robb could potentially threaten the Reach as a way to force his enemy to divide their forces and reverse the Lannisters’ recent advantage in numbers