No. Hardware incompatibility is absolute.
| Aspect | Game Boy Advance (2001) | Nintendo DS (2004) |
|---|---|---|
| CPU | ARM7TDMI @ 16.78 MHz | ARM946E-S @ 67 MHz + ARM7TDMI @ 33 MHz (dual core) |
| RAM | 256 KB WRAM + 96 KB VRAM | 4 MB Main RAM + 656 KB VRAM |
| Screens | 1x 240x160 (Reflective/Backlit) | 2x 256x192 (Touch + Top) |
| Cartridge Slot | GBA Game Pak (32-pin) | DS Card Slot (Top, 45-pin) + GBA Slot (Bottom, 32-pin) |
| Media | Cartridge (Mask ROM / Flash) | DS Card (Mask ROM, 8MB–512MB) |
Physical: DS cards are thinner, different pinout, and keyed differently. They will not fit in a GBA slot.
Game Boy Advance games *do* play on Nintendo DS / DS Lite. The bottom slot (Slot-2) is a native GBA hardware implementation. DS/DS Lite only. DSi / DSi XL / 3DS / 2DS lack the GBA slot and cannot play GBA carts natively (requires CFW/emulation).