Divergent thinking is the key mechanism for generating creative ideas. In collaborative ideation, it leads to the generation of a wide range of creative ideas. But this process can be challenging due to fear of judgment, idea fixation, and the influence of group dynamics. In this paper, we explore how integrating generative language models as an AI peer impacts collaborative divergent thinking. We conducted a randomized controlled experiment (N=96) with four conditions, varying two factors: the structure of idea sharing (live vs. round-based), and the presence of an AI peer generating ideas using a Generative Language Model. Using a mixed-methods approach, we assessed creative fluency, idea elaboration and originality, collaboration, and participants' experience. Results show that AI agents generated more original ideas than human participants, but that exposure to these ideas decreased participants' fluency and originality. Round-based interaction also strengthened collaboration, while decreasing individual fluency.