I think this is a good idea. I don't know how programming works, nor could I ever comprehend how hard of work it is... But, you coudl have restrictions to it.
Toggle On/Off Offline capabilities. The second you post ANYWHERE, send ANY message (That includes responding) then you automatically are put as "Online"
If someone sends a message, their on/off toggle things returns to off, so they are seen as online. And they cant use it again until they log off and log back on.
Personally, I would just love to get on, do my turns, and not be bothered by anyone. Or just watch people chat discreetly.