Not originally. Halo: Combat Evolved launched in 2001; Xbox Live debuted in November 2002. The game shipped with:
It did not support online matchmaking at launch.
Halo: Combat Evolved Anniversary (2011, Xbox 360) and Halo: The Master Chief Collection (2014, Xbox One/PC) added full Xbox Live/online multiplayer support, including matchmaking, dedicated servers, and cross-play. You can now play the original campaign and multiplayer online via these versions.