Privacy and annotation bottlenecks are two major issues that profoundly affect the practicality of machine learning-based medical image analysis. Although significant progress has been made in these areas, these issues are not yet fully resolved. In this paper, we seek to tackle these concerns head-on and systematically explore the applicability of non-contrastive self-supervised learning (SSL) algorithms under federated learning (FL) simulations for medical image analysis. We conduct thorough experimentation of recently proposed state-of-the-art non-contrastive frameworks under standard FL setups. With the SoTA Contrastive Learning algorithm, SimCLR as our comparative baseline, we benchmark the performances of our 4 chosen non-contrastive algorithms under non-i.i.d. data conditions and with a varying number of clients. We present a holistic evaluation of these techniques on 6 standardized medical imaging datasets. We further analyse different trends inferred from the findings of our research, with the aim to find directions for further research based on ours. To the best of our knowledge, ours is the first to perform such a thorough analysis of federated self-supervised learning for medical imaging. All of our source code will be made public upon acceptance of the paper.