Pausing the game does stop everything in the game; however you have to keep a few things in mind about how pausing works in LDW games.

Leaving the game on the menu screen (or any other screen) does not pause the game, even though it seems like nothing is going on.

Going to the Options screen and pausing the game will completely pause the game, but only if you click Done on the Options dialog and quit the game.

If you intend to leave the game running, the safest and most reliable way to pause it is to press the space bar and verify that you see the message "GAME PAUSED" in the blue player comm area.

I always use the space bar to pause the game, since it doesn't matter if you leave it running or quit; it's paused.