I sometimes listen to lectures on my phone using ear buds, but occasionally with only one ear bud in. Is the other half of my brain losing out on any aspect of the lecture? Just how good is the corpus callosum at sharing information between the hemispheres?
Auditory information is routed to cerebral hemispheres via the brainstem and midbrain. Structures in the midbrain receive information from both ears and combine it (including differencing it for spatial location) before sending the combined information on to both cerebral hemispheres. Usually only the left hemisphere interprets the sound for language content, but it is doing so based on the sounds perceived from both ears. The corpus callosum would not be involved in the hearing pathways. So sound coming from the left ear should work as well as sound from the other if the perception level is adequate and not interfered with by sounds from the other ear. It is likely the sound perception is somewhat better if both ears are receiving input from the source.