We are interested in increasing the ability of groups to collaborate efficiently by leveraging new advances in AI and Conversational Agent (CA) technology. Given the longstanding debate on the necessity of embodiment for CAs, bringing them to groups requires answering the questions of whether and how providing a CA with a face affects its interaction with the humans in a group. We explored these questions by comparing group decision-making sessions facilitated by an embodied agent, versus a voice-only agent. Results of an experiment with 20 user groups revealed that while the embodiment improved various aspects of group's social perception of the agent (e.g., rapport, trust, intelligence and power), its impact on the group-decision process and outcome was nuanced. Drawing on both quantitative and qualitative findings, we discuss the pros and cons of embodiment, argue that the value of having a face depends on the types of assistance the agent provides, and lay out directions for future research.