Generative Artificial Intelligence (Gen-AI) models are increasingly used to produce content across domains, including text, images, and audio. While these models represent a major technical breakthrough, they gain their generative capabilities from being trained on enormous amounts of human-generated content, which often includes copyrighted material. In this work, we investigate whether audio watermarking techniques can be used to detect an unauthorized usage of content to train a music generation model. We compare outputs generated by a model trained on watermarked data to a model trained on non-watermarked data. We study factors that impact the model's generation behaviour: the watermarking technique, the proportion of watermarked samples in the training set, and the robustness of the watermarking technique against the model's tokenizer. Our results show that audio watermarking techniques, including some that are imperceptible to humans, can lead to noticeable shifts in the model's outputs. We also study the robustness of a state-of-the-art watermarking technique to removal techniques.