With just a few words, designers can invoke text-to-image AI tools to generate relevant images that jump-start the creative process. These images are computationally generated to approximate everyday-life physical or digital products, such as a coffee machine or a sports website, and thus can aid collaborative design. But how do generative AI tools influence the User Experience (UX) design process, and do they improve product UX after all? This paper investigates the integration of generative AI in the UX design process in the context of mobile application design. We organized two distinct design workshops where eight designers in total (1) used no AI, or (2) the Midjourney AI tool, to design two high-fidelity mobile app prototypes. We evaluated both prototypes with 32 participants in a user study. Our results indicate that AI influences the UX design process in a differential way but it does not necessarily lead to superior UX quality.