Recent work on self-supervised pre-training focus on leveraging large-scale unlabeled speech data to build robust endto-end (E2E) acoustic models (AM) that can be later finetuned on downstream tasks e.g., automatic speech recognition (ASR). Yet, few works investigated the impact on performance when the data substantially differs between the pre-training and downstream fine-tuning phases (i.e., domain shift). We target this scenario by analyzing the robustness of Wav2Vec2.0 and XLS-R models on downstream ASR for a completely unseen domain, i.e., air traffic control (ATC) communications. We benchmark the proposed models on four challenging ATC test sets (signal-to-noise ratio varies between 5 to 20 dB). Relative word error rate (WER) reduction between 20% to 40% are obtained in comparison to hybrid-based state-of-the-art ASR baselines by fine-tuning E2E acoustic models with a small fraction of labeled data. We also study the impact of fine-tuning data size on WERs, going from 5 minutes (few-shot) to 15 hours.