Repository-level code intelligence tasks require large language models (LLMs) to process long, multi-file contexts. Such inputs introduce three challenges: crucial context can be obscured by noise, truncated due to limited windows, and increased inference latency. Context compression mitigates these risks by condensing inputs. While studied in NLP, its applicability to code tasks remains largely unexplored. We present the first systematic empirical study of context compression for repository-level code intelligence, organizing eight methods into three paradigms: discrete token sequences, continuous latent vectors, and visual tokens. We evaluate them on code completion and generation, measuring performance and efficiency. Results show context compression is effective: at 4x compression, continuous latent vector methods surpass full-context performance by up to 28.3% in BLEU score, indicating they filter noise rather than just truncating. On efficiency, all paradigms reduce inference cost. Both visual and text-based compression achieve up to 50% reduction in end-to-end latency at high ratios, approaching the cost of inference without repository context. These findings establish context compression as a viable approach and provide guidance for paradigm selection.