Several recent studies of online social networking platforms have found that adoption rates and engagement levels are positively correlated with structural diversity, the degree of heterogeneity among an individual's contacts as measured by network ties. One common theory for this observation is that structural diversity increases utility, in part because there is value to interacting with people from different network components on the same platform. While compelling, evidence for this causal theory comes from observational studies, making it difficult to rule out non-causal explanations. We investigate the role of structural diversity on retention by conducting a large-scale randomized controlled study on the Twitter platform. We first show that structural diversity correlates with user retention on Twitter, corroborating results from past observational studies. We then exogenously vary structural diversity by altering the set of network recommendations new users see when joining the platform; we confirm that this design induces the desired changes to network topology. We find, however, that low, medium, and high structural diversity treatment groups in our experiment have comparable retention rates. Thus, at least in this case, the observed correlation between structural diversity and retention does not appear to result from a causal relationship, challenging theories based on past observational studies.