Purpose: To propose a task-driven computational framework for assessing diffusion MRI experimental designs which, rather than relying on parameter-estimation metrics, directly measures quantitative task performance. Theory: Traditional computational experimental design (CED) methods may be ill-suited to tasks, such as clinical classification, where outcome does not depend on parameter-estimation accuracy or precision alone. Current assessment metrics evaluate experiments' ability to faithfully recover microstructure parameters rather than their associated task performance. This work proposes a novel CED assessment method that addresses this shortcoming. For a given experimental design (protocol, parameter-estimation method, model, etc.), experiments are simulated start-to-finish and task performance is computed from receiver operating characteristic (ROC) curves and summary metrics such as area under the curve (AUC). Methods: Two experiments were performed: first a validation of the pipeline's task performance predictions in two clinical datasets, comparing in-silico predictions to real-world ROC/AUC; and second, a demonstration of the pipeline's advantages over traditional CED approaches, using two simulated clinical classification tasks. Results: Our computational method accurately predicts (a) the qualitative form of ROC curves, (b) the relative performance of different experimental designs, and (c) the absolute performance (AUC) of each experimental design. Furthermore, our method is shown to outperform traditional task-agnostic assessment methods. Conclusions: The proposed pipeline produces accurate, quantitative predictions of real-world task performance. Compared to current approaches, such task-driven assessment is more likely to identify experimental design that perform well in practice. It provides the foundation for developing future task-driven CED frameworks.