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 and reasoning.