Sparse attention has been claimed to increase model interpretability under the assumption that it highlights influential inputs. Yet the attention distribution is typically over representations internal to the model rather than inputs themselves, suggesting this assumption may not have merit. In this work, we design a set of experiments to help us understand how sparsity affects our ability to use attention as an explainability tool. On three text classification tasks, we verify that only a weak relationship between inputs and co-indexed intermediate representations exists – under sparse attention and otherwise. Further, we do not find any plausible mappings from sparse attention distributions to a sparse set of influential inputs through other avenues. Rather, we observe in this setting that inducing sparsity may make it less plausible that attention can be used as a tool for understanding model behavior.