The success of foundation models in natural language processing and computer vision has motivated similar approaches for general time series analysis. While these models are effective for a variety of tasks, their applicability in medical domains with limited data remains largely unexplored. To address this, we investigate the effectiveness of foundation models in medical time series analysis involving electroencephalography (EEG). Through extensive experiments on tasks such as age prediction, seizure detection, and the classification of clinically relevant EEG events, we compare their diagnostic accuracy with that of specialised EEG models. Our analysis shows that foundation models extract meaningful EEG features, outperform specialised models even without domain adaptation, and localise task-specific biomarkers. Moreover, we demonstrate that diagnostic accuracy is substantially influenced by architectural choices such as context length. Overall, our study reveals that foundation models with general time series understanding eliminate the dependency on large domain-specific datasets, making them valuable tools for clinical practice.