Dark Souls and Demon Souls don't allow you to stop game time through menu access. You simply find a safe zone where you won't be attacked while you're away. Personally, this is not an "immersive" feature, I believe it's there to serve as another bit of the games' challenge. This isn't an appealing feature at all, it's a bit annoying when something important happens outside of the game and you get killed while addressing it. However, the feature is justified in these games' since you can be invaded by online players in most areas of the game, and pausing wouldn't be fair. Then you could say that when you're playing offline you should be able to pause, but that's not the case. Don't know where to go from here...
Simply put, its not an immersive feature, if it serves no purpose, don't do it.