Yes, financial aid will cover your off campus living expenses. Each year students are awarded based on cost of attendance (COA) which includes room and board. Since you will be living off campus you will not be billed for on campus housing, but room and board figures stay in your COA. You may get aid up to your COA, so any remaining credit on your account will be given to you in the form of a refund. That refund can be applied to your off campus expenses.
Also, if you require additional funds a Parent Plus or alternative loan can fill the gap.