This paper examines the degree to which optimizing a lithium-ion battery's cycling for parameter identifiability can improve the robustness of subsequent health-conscious, model-based battery control. The paper builds on two established bodies of literature showing that (i) battery trajectory optimization for identifiability can improve parameter estimation accuracy significantly, and (ii) model-based battery control can improve performance significantly without compromising longevity. To the best of the authors' knowledge, the connection between these two distinct bodies of literature has never been examined before. We highlight the importance of this connection through an illustrative case study. Specifically, we (i) optimize the experimental cycling of commercial lithium-ion battery cells for identifiability. We then (ii) use the optimized cycles for experimental parameter identification, and (iii) use the resulting parameter values for pseudospectral battery charge trajectory optimization. Finally, we (iv) examine the robustness of the resulting solution to battery parameter identification uncertainties generated using Fisher information analysis. The results of this case study are quite compelling: the likelihood of accidental damage via lithium plating diminishes considerably when battery parameters are estimated from an identifiability-optimizing cycle prior to the use of these parameters in health-conscious control.