Noise cancelling headphones tend to make talking worse, not better. They cancel out background rumblings and repetitive noises, like the engine roar. The voices would come through loud and clear, without that roar to hide it.
-D/a
A friend of mine designs cockpit displays at a major airline builder. He said that had never heard the issue come up at his workplace. He did say, however, that there is a lot of emphasis on trying to maintain pilot situational awareness, particularly during takeoff and landing and that if, indeed, something were to make the autopilot kick out or some spurious warning message appear on flight displays, it would definitely be a distraction to make the pilots work through checklists of procedures to diagnose and respond to the issue. He could not rule out that possibility, but designing displays does not - in his case - take such matters into account as a normal course. This tells me that rf signals may have the potential to disturb other systems, but not so much that it has been taken into consideration in the design of cockpit displays. Clearly, however, the FAA errs on the side of caution here, not because of significant evidence, but because of the theoretical possibility. And if it did happen, the evidence would probably go down with the plane.