AI-based face recognition has become increasingly appealing for daily life applications due to its high performance. At the same time, image coding is very commonly used and, thus, many applications perform face recognition with decoded images. However, using decoded images, which may suffer from compression artifacts, may impact the final decision-making process of AI-based face recognition systems and, thus, its overall recognition performance. This paper studies the impact of image coding on the overall face verification performance of a popular and high performing face recognition solution, ArcFace. Face recognition using both original and decoded images, with several compression rates and qualities, is considered. Tests were performed using the Labeled Faces in the Wild (LFW) face dataset, with its images coded using conventional image coding standards, notably JPEG, JPEG 2000, and JPEG XL, as well as three emerging AI-based image codecs. As expected, the experimental results show that coding can have a significant impact on face recognition performance, with its impact becoming increasingly relevant as the coding rate is reduced. It is also observed that the recent AI-based image codecs appear to offer slightly better recognition performance for the same coding rates as a consequence of their better RD performance.