Using DNA molecules for data storage presents a compelling solution to the ever-growing demand for efficient and sustainable data storage systems. DNA offers notable advantages in terms of storage density, longevity, and energy efficiency. This has made the development of effective coding and compression techniques for DNA-based storage a critical research area within signal processing. One particularly challenging aspect is the encoding of multimedia content, such as images, for storage in DNA. JPEG DNA, a recent standardization effort led by the JPEG Committee, addresses this challenge by integrating both source and channel coding. The source coding focuses on data compression, while the channel coding ensures error resilience and accommodates the biochemical constraints of the DNA medium. In this paper, the impact of integrating learning-based source coding into the JPEG DNA framework is explored. This study reveals promising improvements in performance by replacing traditional image compression techniques with a learning-based approach, highlighting the potential for further advancements in DNA-based data storage.