Listeners can adapt to noise-vocoded speech under divided attention using a dual task design [Wang, Chen, Yan, McGettigan, Rosen, and Adank, Trends Hear. 27, 23312165231192297 (2023)]. Adaptation to noise-vocoded speech, an artificial degradation, was largely unaffected for domain-general (visuomotor) and domain-specific (semantic or phonological) dual tasks. The study by Wang et al. was replicated in an online between-subject experiment with 4 conditions (N = 192) using 40 dysarthric sentences, a natural, real-world variation of the speech signal listeners can adapt to, to provide a closer test of the role of attention in adaptation. Participants completed a speech-only task (control) or a dual task, aiming to recruit domain-specific (phonological or lexical) or domain-general (visual) attentional processes. The results showed initial suppression of adaptation in the phonological condition during the first ten trials in addition to poorer overall speech comprehension compared to the speech-only, lexical, and visuomotor conditions. Yet, as there was no difference in the rate of adaptation across the 40 trials for the 4 conditions, it was concluded that perceptual adaptation to dysarthric speech could occur under divided attention, and it seems likely that adaptation is an automatic cognitive process that can occur under load.