The term "connected" is used in two very different ways on mush servers.
A player is said to be "connected" if there is a TCP connection to the mush server that has logged in as a player object. Players that are not connected are typically not visible in rooms.
A room is said to be "connected" if there is a path of exits leading from a player_starting_room (typically #0) to the room, or if the room has the Floating flag set. In some mush configurations, a room is considered connected if it has any exits leading from it. Many mushes warn players on a regular basis about any unconnected rooms they own.