I don’t know. I think that the son of Poseidon will live but have some kind of injury. At the end of The Ship of the Dead, which I think is set after ToA, Annabeth says Percy is as alight as he can be. This could mean that he is grieving Jason’s death, as well as any other major deaths in the last two books, or he suffered some kind of injury.
No, Percy won't die. He's Rick's number one cash cow. Notice how he shoehorns Percy into every story even if he's not needed? That's because Rick knows Percy attracts viewership. If he were to kill Percy, it'd hurt him more than us.