Deep learning (DL) based tools have recently reached performance levels similar to state-of-the-art hand-crafted methods for Point Cloud (PC) coding and classification. In 2022, JPEG issued a Call for Proposals for a Learning-based PC Coding (PCC) standard that envisions a unified representation, targeting both human visualization and computer vision tasks. This paper proposes the first DL-based Compressed Domain PC CLassifier (CD-PCCL), built on the PointGrid classifier, for geometry-only PCs coded with the current DL-based JPEG Pleno PCC Verification Model. The performance of compressed domain PC classification is studied against using voxel domain classification, notably for original, voxelized, and decompressed PCs. Experimental results with the ModelNet40 PC dataset show the proposed CD-PCCL can achieve significant PC classification gains regarding decompressed domain classification, while reducing the PC classifier complexity.