Satellite image restoration aims to improve image quality by compensating for degradations (e.g., noise and blur) introduced by the imaging system and acquisition conditions. As a fundamental preprocessing step, restoration directly impacts both ground-based product generation and emerging onboard AI applications. Traditional restoration pipelines based on sequential physical models are computationally intensive and slow, making them unsuitable for onboard environments. In this paper, we introduce ConvBEERS: a Convolutional Board-ready Embedded and Efficient Restoration model for Space to investigate whether a light and non-generative residual convolutional network, trained on simulated satellite data, can match or surpass a traditional ground-processing restoration pipeline across multiple operating conditions. Experiments conducted on simulated datasets and real Pleiades-HR imagery demonstrate that the proposed approach achieves competitive image quality, with a +6.9dB PSNR improvement. Evaluation on a downstream object detection task demonstrates that restoration significantly improves performance, with up to +5.1% mAP@50. In addition, successful deployment on a Xilinx Versal VCK190 FPGA validates its practical feasibility for satellite onboard processing, with a ~41x reduction in latency compared to the traditional pipeline. These results demonstrate the relevance of using lightweight CNNs to achieve competitive restoration quality while addressing real-world constraints in spaceborne systems.