No, the suitability of a faculty member is not a function of the background of that faculty member alone. Since this question only arises in instances where faculty members have atypical qualifications, it only can be answered in the context of a particular school. Relevant questions focus on the contribution that faculty member is expected to make toward the mission of the school and the cohort of other faculty members in the school. AACSB International accredits programs offered by institutions, it does not certify individuals. A corollary to this is that an atypically prepared faculty member may not have raised questions in one school but could raise questions in another school with a different mission and different faculty composition.