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Back-translation provides a simple yet effective approach to exploit monolingual corpora in Neural Machine Translation (NMT). Its iterative variant, where two opposite NMT models are jointly trained by alternately using a synthetic parallel corpus generated by the reverse model, plays a central role in unsupervised machine translation. In order to start producing sound translations and provide a meaningful training signal to each other, existing approaches rely on either a separate machine translation system to warm up the iterative procedure, or some form of pre-training to initialize the weights of the model. In this paper, we analyze the role that such initialization plays in iterative back-translation. Is the behavior of the final system heavily dependent on it? Or does iterative back-translation converge to a similar solution given any reasonable initialization? Through a series of empirical experiments over a diverse set of warmup systems, we show that, although the quality of the initial system does affect final performance, its effect is relatively small, as iterative back-translation has a strong tendency to convergence to a similar solution. As such, the margin of improvement left for the initialization method is narrow, suggesting that future research should focus more on improving the iterative mechanism itself.