Can You Play CDs on a Wii? No

No. The Wii's optical drive reads only Wii Optical Discs (single/dual-layer, proprietary format similar to DVD). It cannot read standard Audio CDs, CD-ROMs, DVD-Video, or Blu-ray.

For music, use the Photo Channel (SD card → MP3) or stream via Internet Channel (discontinued) / homebrew apps on a modded Wii.