When using Skype as a mobile application, if I'm just logged in but not using it, does it consume data (i.e. Kb) during this log in?
If you are signed in to Skype but not making any calls, Skype will use on average 0-4kbps. When you make a call, Skype will use on average between 24-128kbps.
Of course, it refers to the desktop version, but I think it's a fair assumption to extrapolate it to the mobile client as well. Not the numbers, but only the fact its self. As Alessandro said, it needs to communicate with the serves, otherwise you would not know who's online and who's not.