Speech-based digital biomarkers represent a scalable, non-invasive frontier for the early identification of Mild Cognitive Impairment (MCI). However, the development of robust diagnostic models remains impeded by acute clinical data scarcity and a lack of interpretable reasoning. Current solutions frequently struggle with cross-lingual generalization and fail to provide the transparent rationales essential for clinical trust. To address these barriers, we introduce SynCog, a novel framework integrating controllable zero-shot multimodal data synthesis with Chain-of-Thought (CoT) deduction fine-tuning. Specifically, SynCog simulates diverse virtual subjects with varying cognitive profiles to effectively alleviate clinical data scarcity. This generative paradigm enables the rapid, zero-shot expansion of clinical corpora across diverse languages, effectively bypassing data bottlenecks in low-resource settings and bolstering the diagnostic performance of Multimodal Large Language Models (MLLMs). Leveraging this synthesized dataset, we fine-tune a foundational multimodal backbone using a CoT deduction strategy, empowering the model to explicitly articulate diagnostic thought processes rather than relying on black-box predictions. Extensive experiments on the ADReSS and ADReSSo benchmarks demonstrate that augmenting limited clinical data with synthetic phenotypes yields competitive diagnostic performance, achieving Macro-F1 scores of 80.67% and 78.46%, respectively, outperforming current baseline models. Furthermore, evaluation on an independent real-world Mandarin cohort (CIR-E) demonstrates robust cross-linguistic generalization, attaining a Macro-F1 of 48.71%. These findings constitute a critical step toward providing clinically trustworthy and linguistically inclusive cognitive assessment tools for global healthcare.