Technology influences Open Science (OS) practices, because conducting science in transparent, accessible, and participatory ways requires tools/platforms for collaborative research and sharing results. Due to this direct relationship, characteristics of employed technologies directly impact OS objectives. Generative Artificial Intelligence (GenAI) models are increasingly used by researchers for tasks such as text refining, code generation/editing, reviewing literature, data curation/analysis. GenAI promises substantial efficiency gains but is currently fraught with limitations that could negatively impact core OS values such as fairness, transparency and integrity, and harm various social actors.In this paper, we explore possible positive and negative impacts of GenAI on OS. We use the taxonomy within the UNESCO Recommendation on Open Science to systematically explore the intersection of GenAI and OS. We conclude that using GenAI could advance key OS objectives by further broadening meaningful access to knowledge, enabling efficient use of infrastructure, improving engagement of societal actors, and enhancing dialogue among knowledge systems. However, due to GenAI limitations, it could also compromise the integrity, equity, reproducibility, and reliability of research, while also having potential implications for the political economy of research and its infrastructure. Hence, sufficient checks, validation and critical assessments are essential when incorporating GenAI into research workflows.