This would be one of the cool things that SE could implement for the game.

For example if I am queued in DF for pretty long time I oftenly switch to surf internet or do something else not to sit there and just wait. Ofcourse I turned sounds to be played when the game loses focus so I can hear the notification pop up but I hav eto put my headphones on for it.

In some other games I have seen the taskbar to blink with yellow/red depending on severity of the in-game event like you are being attacked by mobs or some other notifications pops. Though it is a PC specific feature I do not expect it to be implemented asap but I think it would be just great.

In FFXIV I would like to see: DF popup, your character being attacked, Ready check, private chat message