You could, but take into consideration that you would not receive an EFC and some state-school-based aid programs look at the EFC to determine your eligibility for their funds, if you don't have an EFC then you won't be eligible for those aid programs.
And what if my parents live in one of the Freely Associated States?
Ask them to enter the Amount of Wages Earned from their Freely Associated States tax form in the field where the FAFSA form asks for adjusted gross income.
Another doubt I have is, what if my parents do not have a social security number?