No. Game Boy Color (GBC) exclusive cartridges (black, clear, or colored) will not work in the original Game Boy (DMG), Game Boy Pocket, or Game Boy Light.
Some games (e.g., Pokémon Gold/Silver/Crystal, Zelda Oracle titles, Harry Potter games) are Game Boy / Game Boy Color hybrids (gray/black cart with "Game Boy" logo). These run on original GB in monochrome but show color on GBC/GBA.
If it's a black cart with only the GBC logo, you need a GBC, GBA, or GBA SP to play it.