The paper explores the various factors that appear to constrain the implementation in sub-Saharan Africa of the WHO/UNICEF Alma Ata resolutions that member states support the use of indigenous health practitioners in government health programs. It also presents arguments and evidence that suggest ways to overcome the constraining factors. Discussion focuses on traditional healers as distinct from traditional birth attendants. The question posed in the title is not fully answered, but a considerable amount of fact, programmatic experience, and observation related to the issue is assembled and discussed in order to approach an answer, and to inform those who hold a variety of positions with regard to the Alma Ata resolutions.