It's certainly possible to to make use of your other monitors while XCOM is running. Go to Options > Video, set mode to 'borderless window', ensure the resolution is set to your native resolution, and turn off 'lock mouse to window'.
To stop the game from pausing when it loses focus, you need to dive into
...\Steam\steamapps\common\XCom-Enemy-Unknown\Engine\Config (if you're playing the Steam version). Find
bPauseOnLossOfFocus and set it to FALSE. This is a standard Unreal Engine variable so it works on most games made using the engine.
I just tested it and it works perfectly, although after altering the .ini file you might need to change to borderless window mode again after relaunching.