No. Nintendo DS game cards (mask ROM or flash memory with proprietary firmware) cannot be erased and reused for arbitrary data.
Technical Barriers
Hardware Design: Game cards are read-only (mask ROM) or write-once (save data on separate EEPROM/Flash). The game ROM region is physically unalterable.
Encryption/Signing: Nintendo signs each game; the DS/3DS verifies signatures before execution. Unsigned/modified data won't boot.
Bus Protocol: The card interface (SPI-like) expects specific command sequences for game ROM access, not generic mass storage.
What You Can Do
Format Save Data: In System Settings → Data Management, you can erase the save partition (EEPROM/Flash) on the card. The game ROM remains.
Flashcarts (R4, Ace3DS, etc.): These are separate cartridges with microSD slots that run homebrew/ROMs. They don't rewrite original game cards.
Sell/Trade: Original carts retain value; sell to collectors/retro shops.
Recycle: E-waste programs accept cartridges.
Attempting to hack a retail game card risks permanent damage. Use flashcarts or emulation for custom content.