The calculation of shortest-path distances in road networks is a core operation in navigation systems, location-based services, and spatial analytics. Although classical algorithms, e.g., Dijkstra's algorithm, provide exact answers, their latency is prohibitive for modern real-time, large-scale deployments. Over the past two decades, numerous distance indexes have been proposed to speed up query processing for shortest distance queries. More recently, with the advancement in machine learning (ML), researchers have designed and proposed ML-based distance indexes to answer approximate shortest path and distance queries efficiently. However, a comprehensive and systematic evaluation of these ML-based approaches is lacking. This paper presents the first empirical survey of ML-based distance indexes on road networks, evaluating them along four key dimensions: Training time, query latency, storage, and accuracy. Using seven real-world road networks and workload-driven query datasets derived from trajectory data, we benchmark ten representative ML techniques and compare them against strong classical non-ML baselines, highlighting key insights and practical trade-offs. We release a unified open-source codebase to support reproducibility and future research on learned distance indexes.