Given a co-authorship collaboration network, how well can we cluster the participating authors into communities? If we also consider their citation network, based on the same individuals, is it possible to do a better job? In general, given a network with multiple types (or views) of edges (e.g., collaboration, citation, friendship), can community detection and graph clustering benefit? In this work, we propose MULTI-CLUS and GRAPHFUSE, two multi-graph clustering techniques powered by Minimum Description Length and Tensor analysis, respectively. We conduct experiments both on real and synthetic networks, evaluating the performance of our approaches. Our results demonstrate higher clustering accuracy than state-of-the-art baselines that do not exploit the multi-view nature of the network data. Finally, we address the fundamental question posed in the title, and provide a comprehensive answer, based on our systematic analysis.