No, the Nintendo DSi does not have a built-in iPod or iTunes compatibility. It includes a basic Nintendo DSi Sound application for playing AAC (.m4a) files from an SD card.
/music/ on SD root. Place .m4a files inside. Subfolders work for albums.The DSi Shop (closed March 2017) sold a few Nintendo DSi Sound apps (e.g., Mario Paint Composer, Korg DS-10 synth), not commercial music tracks.
Verdict: The DSi is a poor music player by modern standards. Use a phone, dedicated DAP, or even a 2005 iPod Nano for a vastly better experience.