And they did.
I did animal rescue in NOLA, and it was amazing to watch as 5 dogs and 3 cats -- none of which knew each other -- could be piled into the back seat of a sedan and they didn't kill each other because they KNEW they had been rescued from a disaster. They knew they had a choice to either "deal with the opposite species in the back seat of this car or perish on the streets of NOLA." In every case that I know of, these frightened animals of predator/prey species got along fine in the midst of the rescue.
Hah...! what an interesting vignette... thanks for sharing it.