According to other people's experiences I've read, it has happened, so I am assuming it is a rare thing that happens. For example, Devynn became a siren whenever she went.
あなた become who you're meant to be for most people, but あなた have to unlock that part inside of you. My personal experience is different, because in some dreams I'm a mermaid, others I have wings, and some I'm just a normal ロスト girl. it changes with different people, so your experience may be different