Setting up Split-screen\n\n Players can now start MW2, and once they reach the main menu, the second player should press the prompted button to join the game (X for PlayStation, A for Xbox, or Space for K/M). At this point, the second player must either log into their Activision ID profile or play without one.

Late answer, but yes. You'll want to go to "Private Match" (which you can play alone or with friends, including split-screen co-op if you'd like to play with a local friend or family). You can play any of the modes here, but if you want bots, you'll need to go to Game Settings < Bots, then configure as you wish.