Technological advancements in deep learning for speech and voice have contributed to a recent expansion in applications for voice cloning, synthesis and generation. Invisibilised stakeholders in this expansion are numerous absent bodies, whose voices and voice data have been integral to the development and refinement of these speech technologies. This position paper probes current working practices for voice and speech in machine learning and AI, in which the bodies of voices are "invisibilised". We examine the facts and concerns about the voice-Body in applications of AI-voice technology. We do this through probing the wider connections between voice data and Schaefferian listening; speculating on the consequences of missing Bodies in AI-Voice; and by examining how vocalists and artists working with synthetic Bodies and AI-voices are 'bringing the Body back' in their own practices. We contribute with a series of considerations for how practitioners and researchers may help to 'bring the Body back' into AI-voice technologies.