Yes, someone has to be logged in to initiate any contact with them - pm, friend request, fc invite... I'm not sure but following them on Lodestone *may* let you know when they log in. I know it shows you when people in your FC log in.
http://na.finalfantasyxiv.com/lodest...acter/1271238/ - this is for Enkidoh
http://na.finalfantasyxiv.com/lodest...acter/6632159/ - this is for Pyro