Early diagnosis of Alzheimer's Disease (AD) is crucial for delaying its progression. While AI-based speech detection is non-invasive and cost-effective, it faces a critical data efficiency dilemma due to medical data scarcity and privacy barriers. Therefore, we propose FAL-AD, a novel framework that synergistically integrates federated learning with data augmentation to systematically optimize data efficiency. Our approach delivers three key breakthroughs: First, absolute efficiency improvement through voice conversion-based augmentation, which generates diverse pathological speech samples via cross-category voice-content recombination. Second, collaborative efficiency breakthrough via an adaptive federated learning paradigm, maximizing cross-institutional benefits under privacy constraints. Finally, representational efficiency optimization by an attentive cross-modal fusion model, which achieves fine-grained word-level alignment and acoustic-textual interaction. Evaluated on ADReSSo, FAL-AD achieves a state-of-the-art multi-modal accuracy of 91.52%, outperforming all centralized baselines and demonstrating a practical solution to the data efficiency dilemma. Our source code is publicly available at https://github.com/smileix/fal-ad.