Low-overlap point cloud registration (PCR) remains a significant challenge in 3D vision. Traditional evaluation metrics, such as Maximum Inlier Count, become ineffective under extremely low inlier ratios. In this paper, we revisit the registration result evaluation problem and identify the Decision version of the PCR task as the fundamental problem. To address this Decision PCR task, we propose a data-driven approach. First, we construct a corresponding dataset based on the 3DMatch dataset. Then, a deep learning-based classifier is trained to reliably assess registration quality, overcoming the limitations of traditional metrics. To our knowledge, this is the first comprehensive study to address this task through a deep learning framework. We incorporate this classifier into standard PCR pipelines. When integrated with our approach, existing state-of-the-art PCR methods exhibit significantly enhanced registration performance. For example, combining our framework with GeoTransformer achieves a new SOTA registration recall of 86.97\% on the challenging 3DLoMatch benchmark. Our method also demonstrates strong generalization capabilities on the unseen outdoor ETH dataset.