We consider the problem of pilot-aided, uplink channel estimation in a distributed massive multiple-input multiple-output (MIMO) architecture, in which the access points are connected to a central processing unit via fiber-optical fronthaul links, carrying a two-level-quantized version of the received analog radio-frequency signal. We adapt to this architecture the deep-learning-based channel-estimation algorithm recently proposed by Nguyen et al. (2023), and explore its robustness to the additional signal distortions (beyond 1-bit quantization) introduced in the considered architecture by the automatic gain controllers (AGCs) and by the comparators. These components are used at the access points to generate the two-level analog waveform from the received signal. Via simulation results, we illustrate that the proposed channel-estimation method outperforms significantly the Bussgang linear minimum mean-square error channel estimator, and it is robust against the additional impairments introduced by the AGCs and the comparators.