The ubiquity of microphone-enabled devices has lead to large amounts of unlabelled audio data being produced at the edge. The integration of self-supervised learning (SSL) and federated learning (FL) into one coherent system can potentially offer data privacy guarantees while also advancing the quality and robustness of speech representations. In this paper, we provide a first-of-its-kind systematic study of the feasibility and complexities for training speech SSL models under FL scenarios from the perspective of algorithms, hardware, and systems limits. Despite the high potential of their combination, we find existing system constraints and algorithmic behaviour make SSL and FL systems nearly impossible to build today. Yet critically, our results indicate specific performance bottlenecks and research opportunities that would allow this situation to be reversed. While our analysis suggests that, given existing trends in hardware, hybrid SSL and FL speech systems will not be viable until 2027. We believe this study can act as a roadmap to accelerate work towards reaching this milestone much earlier.