Recent years have witnessed a paradigm shift in deep learning from task-centric model design to task-agnostic representation learning and task-specific fine-tuning. Pretrained model representations are commonly evaluated extensively across various real-world tasks and used as a foundation for different downstream tasks. This paper proposes a solution for assessing the quality of representations in a task-agnostic way. To circumvent the need for real-world data in evaluation, we explore the use of synthetic binary classification tasks with Gaussian mixtures to probe pretrained models and compare the robustness-accuracy performance on pretrained representations with an idealized reference. Our approach offers a holistic evaluation, revealing intrinsic model capabilities and reducing the dependency on real-life data for model evaluation. Evaluated with various pretrained image models, the experimental results confirm that our task-agnostic evaluation correlates with actual linear probing performance on downstream tasks and can also guide parameter choice in robust linear probing to achieve a better robustness-accuracy trade-off.