Not necessarily. Your school's financial aid office determines your eligibility and will reward you the direct loan (at a minimum) if they are able to process the FAFSA. You need to find out when they stop processing financial aid applications.
This is completely dependent upon your school. Most schools have spent a good portion of their institutional funding at such a late date, but it's possible that your school sets money aside for late accepts. You need to work with your financial aid office directly if you have questions.
First, congratulations on your acceptance. Second, fill out the FAFSA ASAP, and call your school's financial aid coordinator. Most schools have a dedicated coordinator for the dental school, so call student services and make an appointment as soon as you can (before your break ends...)