Yes, those alerts can cause accidents and deaths not related to the nature of those alerts themselves, like driving accidents and heart attacks.
Moreover, since the alerts are all or nothing -- you cannot turn off the sound -- it causes many people to turn them off who would otherwise leave them on. Therefore, they in fact allow deaths and crimes that would otherwise be prevented by these very alerts if they would allow user adjustments like turning off the sound.
The man who would have seen that alert about the kidnapped kid 10 minutes or 1 hour after the alert was sent instead of 1 second after, now would not see that alert at all because he had to turn it off completely to avoid affecting his job and his sanity.
Students, movie goers, restaurant goers, doctors, workers in hundreds of different situations, all need to turn these off because these alerts break through all silence settings unless you turn them off completely. Especially when the amber alerts are often not precise and relate to some incident 500 miles away. And then the kidnapped kid has to do without the help he otherwise would have received. So in being so pushy these alerts ironically do more harm than good.
Then there is that recent lawsuit about the ruptured eardrums caused by an alert... What I am suggesting is just the tip of the iceberg.