LiDAR-based localization and SLAM often rely on iterative matching algorithms, particularly the Iterative Closest Point (ICP) algorithm, to align sensor data with pre-existing maps or previous scans. However, ICP is prone to errors in featureless environments and dynamic scenes, leading to inaccurate pose estimation. Accurately predicting the uncertainty associated with ICP is crucial for robust state estimation but remains challenging, as existing approaches often rely on handcrafted models or simplified assumptions. Moreover, a few deep learning-based methods for localizability estimation either depend on a pre-built map, which may not always be available, or provide a binary classification of localizable versus non-localizable, which fails to properly model uncertainty. In this work, we propose a data-driven framework that leverages deep learning to estimate the registration error covariance of ICP before matching, even in the absence of a reference map. By associating each LiDAR scan with a reliable 6-DoF error covariance estimate, our method enables seamless integration of ICP within Kalman filtering, enhancing localization accuracy and robustness. Extensive experiments on the KITTI dataset demonstrate the effectiveness of our approach, showing that it accurately predicts covariance and, when applied to localization using a pre-built map or SLAM, reduces localization errors and improves robustness.