Yes, you can play both the campaign mode and multiplayer mode in Call of Duty: Modern Warfare 3 offline. The campaign mode can be played in its entirety in offline mode, and a Private Multiplayer mode allows you to access all of the maps and modes present in Multiplayer.

Modern Warfare 3 has perhaps the worst Call of Duty single-player campaign I've played. It's shallow, dull, and plays less like the greatest hits and more like underbaked cover versions of missions past.