Large Language Models (LLMs) can produce verbalized self-explanations, yet prior studies suggest that such rationales may not reliably reflect the model's true decision process. We ask whether these explanations nevertheless help users predict model behavior, operationalized as counterfactual simulatability. Using StrategyQA, we evaluate how well humans and LLM judges can predict a model's answers to counterfactual follow-up questions, with and without access to the model's chain-of-thought or post-hoc explanations. We compare LLM-generated counterfactuals with pragmatics-based perturbations as alternative ways to construct test cases for assessing the potential usefulness of explanations. Our results show that self-explanations consistently improve simulation accuracy for both LLM judges and humans, but the degree and stability of gains depend strongly on the perturbation strategy and judge strength. We also conduct a qualitative analysis of free-text justifications written by human users when predicting the model's behavior, which provides evidence that access to explanations helps humans form more accurate predictions on the perturbed questions.