Yes. The Nintendo 3DS is **fully backward compatible** with Nintendo DS cartridges.
Insert the Band Hero DS Game Card into the 3DS cartridge slot.
It will appear on the Home Menu as a DS title (black border).
Launch and play normally.
Caveats
Guitar Grip Peripheral: The DS Guitar Grip (slot-2/GBA slot) **does not fit** the 3DS (no GBA slot). You **cannot** use the official guitar controller on 3DS/2DS.
Controls: You must use the **touchscreen + face buttons** (Default: D-Pad/ABXY for frets, Touchscreen strum). This is significantly harder.
DSi Enhanced Features: None for this title.
Save Data: Stored on the cartridge (same as DS).
Recommendation: Play on an original DS/DS Lite with the Guitar Grip for the intended experience. The 3DS works only as a last resort with touchscreen controls.