The rapid diffusion of generative artificial intelligence (AI) in higher education has reshaped academic practices, yet its implications for transparency, authorship, and academic performance remain insufficiently understood. This study analyzes 4,489 student projects submitted between 2022 and 2025 to investigate the relationship between self-reported AI use, linguistic characteristics of student writing, and academic achievement. Using mixed-effects regression models and a comprehensive institutional dataset, we assess to what extent declared AI use, overall academic achievement, demographic variables, and text readability metrics predict project grades. The findings show that declared AI use is not systematically associated with higher or lower marks once contextual factors are controlled for, while overall performance, attempt number, linguistic complexity, and submission length emerge as robust predictors. The results highlight the importance of nuanced, evidence-based institutional policies that balance ethical AI integration with the safeguarding of academic integrity. By offering a large-scale empirical examination of declared AI usage in authentic coursework, this study contributes critical insights for universities navigating the pedagogical and regulatory challenges of AI-supported learning.