Well, usually there has to be a SIM card in your phone to use it for communication. That SIM card has an ID and sooner or later there is going to be a correlateable pattern - the location of a phone which happens to be close to you very often or simply a voice that can be identified as yours. It depends if NSA wants you and then figures out your alter egos or if its the alter ego they care first about and then they'll try to figure out who's the real ego.

What's the satisfaction to be 100% untraceable anyway? The practially and politically relevant idea is to not cater your data to them.