Event cameras have the ability to capture asynchronous per-pixel brightness changes, called "events", offering advantages over traditional frame-based cameras for computer vision applications. Efficiently coding event data is critical for transmission and storage, given the significant volume of events. This paper proposes a novel double deep learning-based architecture for both event data coding and classification, using a point cloud-based representation for events. In this context, the conversions from events to point clouds and back to events are key steps in the proposed solution, and therefore its impact is evaluated in terms of compression and classification performance. Experimental results show that it is possible to achieve a classification performance of compressed events which is similar to one of the original events, even after applying a lossy point cloud codec, notably the recent learning-based JPEG Pleno Point Cloud Coding standard, with a clear rate reduction. Experimental results also demonstrate that events coded using JPEG PCC achieve better classification performance than those coded using the conventional lossy MPEG Geometry-based Point Cloud Coding standard. Furthermore, the adoption of learning-based coding offers high potential for performing computer vision tasks in the compressed domain, which allows skipping the decoding stage while mitigating the impact of coding artifacts.