To be honest, if they log on and stay invisible(not available for chat) then I cannot see how you could find out for sure? Perhaps if they use the Windows Live Messenger or something like that, and if it's connected to their hotmail, then if they sign into hotmail it'll appear on windows live messenger that they've signed in, so long as you have them connected to your messenger account?
Thats about as much as I know. Maybe someone else can help you further?