I think so. At that point, the candidate says he's bilingual. Based on the information he submits to support his statement, the people reviewing his appointment can say whether they're satisfied.
I gave the example of a person who has degrees from a francophone university and an anglophone university. There's also the example of a person who, as everyone knows, argues in both English and French before the courts, or the example of a federal court judge who regularly hears cases in both languages. In these instances, I don't think it would be necessary to give the person in question a language test.