The examples of cognitive overload discussed seem to focus on someone who's focused on a specific task they believe is going normally, to the exclusion of an input that would have warned them it wasn't.
I wonder how well the theory applies to someone who realizes something's wrong but doesn't know what it is. It seems to me that when you go into troubleshooting mode, as the AF 447 pilots apparently did, you're more likely to step back and look/listen for clues that might explain what's wrong.