Cochlear implants (CIs) are auditory prostheses that restore hearing via electrical stimulation of the auditory nerve. Compared to normal acoustic hearing, sounds transmitted through the CI are spectro-temporally degraded, causing difficulties in challenging listening tasks such as speech intelligibility in noise and perception of music. In normal hearing (NH), musicians have been shown to better perform than non-musicians in auditory processing and perception, especially for challenging listening tasks. This ‘musician effect’ was attributed to better processing of pitch cues, as well as better overall auditory cognitive functioning in musicians. Does the musician effect persist when pitch cues are degraded, as it would be in signals transmitted through a CI? To answer this question, NH musicians and non-musicians were tested while listening to unprocessed signals or to signals processed by an acoustic CI simulation. The task increasingly depended on pitch perception: 1) speech intelligibility (words and sentences) in quiet or in noise, 2) vocal emotion identification, and 3) melodic contour identification. For speech perception, there was no musician effect with the unprocessed stimuli, and a small musician effect only for word identification in one noise condition, in the CI simulation. For emotion identification, there was a small musician effect for both. For melodic contour identification, there was a large musician effect for both. Overall, the effect was stronger as the importance of pitch in the listening task increased. This suggests that the musician effect may be more rooted in pitch perception, rather than in a global advantage in cognitive processing (in which musicians would have performed better in all tasks). The results further suggest that musical training before (and possibly after) implantation might offer some advantage in pitch processing that could partially benefit speech perception, and more strongly emotion and music perception.