The rapid growth on the amount of generated 3D data, particularly in the form of Light Detection And Ranging (LiDAR) point clouds (PCs), poses very significant challenges in terms of data storage, transmission, and processing. Point cloud (PC) representation of 3D visual information has shown to be a very flexible format with many applications ranging from multimedia immersive communication to machine vision tasks in the robotics and autonomous driving domains. In this paper, we investigate the performance of four reference 3D object detection techniques, when the input PCs are compressed with varying levels of degradation. Compression is performed using two MPEG standard coders based on 2D projections and octree decomposition, as well as two coding methods based on Deep Learning (DL). For the DL coding methods, we used a Joint Photographic Experts Group (JPEG) reference PC coder, that we adapted to accept LiDAR PCs in both Cartesian and cylindrical coordinate systems. The detection performance of the four reference 3D object detection methods was evaluated using both pre-trained models and models specifically trained using degraded PCs reconstructed from compressed representations. It is shown that LiDAR PCs can be compressed down to 6 bits per point with no significant degradation on the object detection precision. Furthermore, employing specifically trained detection models improves the detection capabilities even at compression rates as low as 2 bits per point. These results show that LiDAR PCs can be coded to enable efficient storage and transmission, without significant object detection performance loss.