We propose a simple, data-efficient pipeline that augments an implicit reconstruction network based on neural SDF-based CAD parts with a part-segmentation head trained under PartField-generated supervision. Unlike methods tied to fixed taxonomies, our model accepts meshes with any number of parts and produces coherent, geometry-aligned labels in a single pass. We evaluate on randomly sampled CAD meshes from the ABC dataset with intentionally varied part cardinalities, including over-segmented shapes, and report strong performance across reconstruction (CDL1/CDL2, F1-micro, NC) and segmentation (mIoU, Accuracy), together with a new Segmentation Consistency metric that captures local label smoothness. We attach a lightweight segmentation head to the Flat-CAD SDF trunk; on a paired evaluation it does not alter reconstruction while providing accurate part labels for meshes with any number of parts. Even under degraded reconstructions on thin or intricate geometries, segmentation remains accurate and label-coherent, often preserving the correct part count. Our approach therefore offers a practical route to semantically structured CAD meshes without requiring curated taxonomies or exact palette matches. We discuss limitations in boundary precision, partly due to per-face supervision, and outline paths toward boundary-aware training and higher resolution labels.