The success of learning-based coding techniques and the development of learning-based image coding standards, such as JPEG-AI, point towards the adoption of such solutions in different fields, including the storage of biometric data, like fingerprints. However, the peculiar nature of learning-based compression artifacts poses several issues concerning their impact and effectiveness on extracting biometric features and landmarks, e.g., minutiae. This problem is utterly stressed by the fact that most models are trained on natural color images, whose characteristics are very different from usual biometric images, e.g, fingerprint or iris pictures. As a matter of fact, these issues are deemed to be accurately questioned and investigated, being such analysis still largely unexplored. This study represents the first investigation about the adaptability of learning-based image codecs in the storage of fingerprint images by measuring its impact on the extraction and characterization of minutiae. Experimental results show that at a fixed rate point, learned solutions considerably outperform previous fingerprint coding standards, like JPEG2000, both in terms of distortion and minutiae preservation. Indeed, experimental results prove that the peculiarities of learned compression artifacts do not prevent automatic fingerprint identification (since minutiae types and locations are not significantly altered), nor do compromise image quality for human visual inspection (as they gain in terms of BD rate and PSNR of 47.8% and +3.97dB respectively).