Artificial intelligence (AI) transforms how K-12 schools manage learning, instruction, and enact leadership, often without comprehensive theoretical guidance. This study critically examines whether ten foundational leadership and organisational behavioural theories remain analytically viable and practically relevant in AI-mediated educational contexts. Employing a conceptual analysis grounded in critical theory and interdisciplinary AI literature, the study evaluates each theory's responsiveness to four conceptual pressures introduced by AI: epistemic disruption, relational mediation, ethical opacity, and diminished human agency. The analysis reveals that while instructional leadership and self-efficacy theories align well with AI's strengths in feedback and personalization, others—such as social justice leadership theory and trust theory—experience conceptual strain. A concentric framework is introduced to assess theoretical adaptability, followed by a five-stage model for improving leadership and organisational behavioural theory. AI is not merely a technological tool but a conceptual stress test for leadership and organisational behavioural theory. This study offers a roadmap for extending and re-contextualizing leadership models to address AI-mediated education's ethical, epistemological, and operational demands. It calls on the education leadership field to shift from theory preservation to theory evolution to remain relevant in an algorithmically governed future.