This question appears to be about the social or religious implications of polygamy within church leadership structures, rather than a direct medical or scientific query. In many mainstream Christian denominations, polygamy (being married to more than one person simultaneously) is not accepted. Therefore, individuals practicing polygamy would generally not be eligible for church leadership positions, as these roles often require adherence to specific marital standards outlined in religious texts or doctrines. The side effects, in this context, are primarily exclusion from leadership roles and potential disciplinary action if the practice is discovered and violates church law.