Exploring scientific datasets with billions of samples in real-time visualization presents a challenge - balancing high-fidelity rendering with speed. This work introduces a neural accelerated renderer, NARVis, that uses the neural deferred rendering framework to visualize large-scale scientific point cloud data. NARVis augments a real-time point cloud rendering pipeline with high-quality neural post-processing, making the approach ideal for interactive visualization at scale. Specifically, we render the multi-attribute point cloud using a high-performance multi-attribute rasterizer and train a neural renderer to capture the desired post-processing effects from a conventional high-quality renderer. NARVis is effective in visualizing complex multidimensional Lagrangian flow fields and photometric scans of a large terrain as compared to the state-of-the-art high-quality renderers. Extensive evaluations demonstrate that NARVis prioritizes speed and scalability while retaining high visual fidelity. We achieve competitive frame rates of $>$126 fps for interactive rendering of $>$350M points (i.e., an effective throughput of $>$44 billion points per second) using ~12 GB of memory on RTX 2080 Ti GPU. Furthermore, NARVis is generalizable across different point clouds with similar visualization needs and the desired post-processing effects could be obtained with substantial high quality even at lower resolutions of the original point cloud, further reducing the memory requirements.