Manufacturability assessment is a critical step in bridging the persistent gap between design and production. While artificial intelligence (AI) has been widely applied to this task, most existing frameworks rely on geometry-driven methods that require extensive preprocessing, suffer from information loss, and offer limited interpretability. This study proposes a methodology that evaluates manufacturability directly from parametric design features, enabling explicit incorporation of dimensional tolerances without requiring computer-aided design (CAD) processing. The approach employs Kolmogorov-Arnold Networks (KANs) to learn functional relationships between design parameters, tolerances, and manufacturability outcomes. A synthetic dataset of 300,000 labeled designs is generated to evaluate performance across three representative scenarios: hole drilling, pocket milling, and combined drilling-milling, while accounting for machining constraints and design-for-manufacturing (DFM) rules. Benchmarking against fourteen machine learning (ML) and deep learning (DL) models shows that KAN achieves the highest performance in all scenarios, with AUC values of 0.9919 for drilling, 0.9841 for milling, and 0.9406 for the combined case. The proposed framework provides high interpretability through spline-based functional visualizations and latent-space projections, enabling identification of the design and tolerance parameters that most strongly influence manufacturability. An industrial case study further demonstrates how the framework enables iterative, parameter-level design modifications that transform a non-manufacturable component into a manufacturable one.