Though Annabeth can be a leader will just focus on Percy and Jason...
Percy Jackson was very loyal to his friends, loyalty is his fatal flow,thta even his life he will give in order to save a friend... We have already know Percy's attitude as a leader of camp half-blood, he can be trust... He even became the Praetor of the Twelfth Legion Fulminata...
but then...
Jason Grace is a natural leader, a son of king of gods, the Praetor of the First Legion... He has the sense of duty, his fatal flaw... though Jason is just a recent character, he tends to be a responsible leader...
It is said that Annabeth Chase is a problem for the quest but as Percy, He is loyal to his friend and will not let them down while Jason is disciplene and warlike Roman that might choose to let Annabeth away for the safety of others... It is interesting if the two would have a clash or become a duo leader that is a threat for Gaea