Minimize and/or Close undocked Chat contact list to system tray with a different icon

It is great that I can undock the Chat tab as a separate contact-list window. But it would also be nice to be able to minimize/close this undocked window to system tray (with a different icon than the main application which is already minimized/closed to system tray).

That way, one can use the benefit of undocked contact list (not having to open the main application to start sending a message to someone); and yet have an uncluttered task bar.

Is this possible?