NTA
The aircraft already has something that displays this info, the FPV. Unfortunately, the information from the giros is subject to drift and is also very eratic in its raw state. For that reason it is damped by baro data, otherwise it would be effectively unuseable. If your ADRs are shot then your baro data is unreliable or erroneous and so the data from the giros becomes unuseable which is why the FPV cannot be used with unreliable baro data (as the crew of 447 had at least at first). Thus, your gadget, whilst a good idea on the face of it would suffer from the same issues and thus be of no use in the situation the were in.