This study presents the first systematic evaluation of automated speech recognition (ASR) systems for assessing the intelligibility of Russian-language esophageal voice (EV) in voice and speech rehabilitation following surgical treatment of laryngeal cancer. EV, produced without vocal folds, poses significant acoustic and articulatory challenges for speech recognition systems. We investigate two ASR platforms—Caesar-R, optimized for Russian, and Google Cloud Speech-to-Text, a multilingual cloud-based system—by comparing their transcription performance across three groups: healthy speakers, patients after oral cancer surgery, and post-laryngectomy patients using EV. Speech material included standard diagnostic phrases, phonetically balanced sentences, and vowel phonations. Recognition quality was measured using the Levenshtein distance to quantify transcription errors. Results show that both systems can process EV, though accuracy decreases proportionally to the extent of surgical intervention. Notably, some EV samples were recognized without errors, demonstrating feasibility for objective assessment. These findings support the use of ASR as a scalable, non-invasive tool for tracking EV intelligibility in Russian-language rehabilitation, including offline applications in settings with limited internet access.