Depth perception models are typically trained on non-interactive datasets with predefined camera trajectories. However, this often introduces systematic biases into the learning process correlated to specific camera paths chosen during data acquisition. In this paper, we investigate the role of how data is collected for learning depth completion, from a robot navigation perspective, by leveraging 3D interactive environments. First, we evaluate four depth completion models trained on data collected using conventional navigation techniques. Our key insight is that existing exploration paradigms do not necessarily provide task-specific data points to achieve competent unsupervised depth completion learning. We then find that data collected with respect to photometric reconstruction has a direct positive influence on model performance. As a result, we develop an active, task-informed, depth uncertainty-based motion planning approach for learning depth completion, which we call DEpth Uncertainty-guided eXploration (DEUX). Training with data collected by our approach improves depth completion by an average greater than 18% across four depth completion models compared to existing exploration methods on the MP3D test set. We show that our approach further improves zero-shot generalization, while offering new insights into integrating robot learning-based depth estimation.