Guild Wars 2

I think it would be great to be able to use the to when offline to check on orders and be able to keep playing the market when you don’t have access to the game

One day, it probably will be a feature, though with development of the v2 API being so slow, I wouldn’t expect to see it for several years.

For now however, you can do what you want by simply leaving the game running and using its session to access the API used by the trading post. Any feature that involves actual item interaction cannot be used however since it relies on another API which is handled by the client. In order to access that externally, you have to modify a little javascript.