I´m not familiar with the Air Data Logic at Boeing 737. At Airbus, there should be some kind of ADR Disagree Warning, resulting in Manual Flight and Manual Thrust - but nevertheless a horrable scenario for the crew.
Manual flight and Manual thrust should not be "horrible" for any jet crew, regardless of type. If it is then there is something wrong with the training system. More and more jets are crashing because of pilot's inability to safely fly manually at the basic level.
Magenta lines and computers are all well and good but when it counts, you need to be able to competently cope with none of the goodies. And the more the system tries to hide behind automation to stop manipulation accidents, the worse the accident rate will become.