Automated program comprehension underpins many software engineering tasks, from code summarisation to clone detection. Recent deep learning models achieve strong results but typically rely on source code alone, overlooking contextual information such as version history or structural relationships. This limits their ability to capture how code evolves and operates. We conduct an empirical study on how enriching code representations with such contextual signals affects neural model performance on key comprehension tasks. Two downstream tasks, code clone detection and code summarisation, are evaluated using SeSaMe (1,679 Java methods) and CodeSearchNet (63,259 methods). Five representative models (CodeBERT, GraphCodeBERT, CodeT5, PLBART, ASTNN) are fine-tuned under code-only and context-augmented settings. Results show that context generally improves performance: version history consistently boosts clone detection (e.g., CodeT5 +15.92% F1) and summarisation (e.g., GraphCodeBERT +5.56% METEOR), while call-graph effects vary by model and task. Combining multiple contexts yields further gains (up to +21.48% macro-F1). Human evaluation on 100 Java snippets confirms that context-augmented summaries are significantly preferred for Accuracy and Content Adequacy (p <= 0.026; |delta| up to 0.55). These findings highlight the potential of contextual signals to enhance code comprehension and open new directions for optimising contextual encoding in neural SE models.