I don't think it's possible for software to tell the difference between a corrupt file and an unsupported file type. In both cases, what the software sees is that it is unable to open the file. The error message "could" say something like:
"Audacity cannot open this file. It is either not a supported format or is damaged. You need to convert it to a properly formed audio file of a supported type"
However, the last part of that is surely superfluous - nobody would expect Audacity to support corrupt files. So that just leaves the addition of "or is damaged". In the vast majority of cases, the problem is not due to the file being damaged, but due to the file being an unsupported type.
What would you suggest the error message should be?