Imbuing Large Language Models (LLMs) with specific personas is prevalent for tailoring interaction styles, yet the impact on underlying cognitive capabilities remains unexplored. We employ the Neuron-based Personality Trait Induction (NPTI) framework to induce Big Five personality traits in LLMs and evaluate performance across six cognitive benchmarks. Our findings reveal that persona induction produces stable, reproducible shifts in cognitive task performance beyond surface-level stylistic changes. These effects exhibit strong task dependence: certain personalities yield consistent gains on instruction-following, while others impair complex reasoning. Effect magnitude varies systematically by trait dimension, with Openness and Extraversion exerting the most robust influence. Furthermore, LLM effects show 73.68% directional consistency with human personality-cognition relationships. Capitalizing on these regularities, we propose Dynamic Persona Routing (DPR), a lightweight query-adaptive strategy that outperforms the best static persona without additional training.