asAs far as i remember reading it, Thalia was afraid of heights. itsIts not because she didn't know she was a demigod. So if Percy had a fear of water or of drowning,(I think it's called Aqua-phobia?) then he could die as we see in son of Neptune book where he is sucked into a bog and his powers were also not working properly. So i guess that means Percy wouldn't have died even if he didn't know he was a demigod but rather he would have died if he was phobic like Thalia. Also, I don't think Percy might have died in your hypothetical scenario because even if he didn't want to recognize him as his son, he would have helped him indirectly through naiads or some other sea creatures.