Multimodal Large Language Models (MLLMs) have shown promise in single-agent vision tasks, yet benchmarks for evaluating multi-agent collaborative perception remain scarce. This gap is critical, as multi-drone systems provide enhanced coverage, robustness, and collaboration compared to single-sensor setups. Existing multi-image benchmarks mainly target basic perception tasks using high-quality single-agent images, thus failing to evaluate MLLMs in more complex, egocentric collaborative scenarios, especially under real-world degraded perception conditions. To address these challenges, we introduce AirCopBench, the first comprehensive benchmark designed to evaluate MLLMs in embodied aerial collaborative perception under challenging perceptual conditions. AirCopBench includes 14.6k+ questions derived from both simulator and real-world data, spanning four key task dimensions: Scene Understanding, Object Understanding, Perception Assessment, and Collaborative Decision, across 14 task types. We construct the benchmark using data from challenging degraded-perception scenarios with annotated collaborative events, generating large-scale questions through model-, rule-, and human-based methods under rigorous quality control. Evaluations on 40 MLLMs show significant performance gaps in collaborative perception tasks, with the best model trailing humans by 24.38% on average and exhibiting inconsistent results across tasks. Fine-tuning experiments further confirm the feasibility of sim-to-real transfer in aerial collaborative perception.