There are a few ‘need aware’ schools that do consider your ability to pay while in the admissions process. MOST schools are need blind and they will admit you without knowing if you need FA or not.
For need aware schools, it doesn’t mean they will reject you just because you applied for FA. They’d look at your FA application and decide first if you qualify for FA and second if they admit you how much they will provide. Just because you apply for FA doesn’t mean you’ll get it.