A few GC games require audio to be streamed from the disc. Here's a partial list: Eternal Darkness,Ikaruga,Star Fox Adventures, 1080° Avalanche, Geist, Wave Race: Bluestorm.
Depending on what streamed audio is used for, having no sound can seriously impact the gameplay experience. For some games (e.g. Ikaruga), the audio streams are used for background music. Others use streamed audio for dialog (e.g. Star Fox Adventures). Without audio streaming support, these games will play with muted sound in place of the streamed audio; however, other sound effects may still be present. Legend of Zelda: Collectors Disk only uses audio streaming for the selection screen, so the muted audio has no impact on the games themselves.
Although I do not understand the hardware details, I do know that at present the only solution for audio streaming with backups is installing a modchip on a compatible drive, and only a few modchips have fully working audio streaming support (e.g. YAOSM, Wiinja, Wiikey v1). Thus far, I've found that the audio streaming fix only works properly on DMS/D2A/D2B drives - D2C/D2C2/D2E have playback issues, and D3-2/D4 do not read backups.