No. Navy will not reimburse you for WREB or any other regional licensure exam. The Navy will only reimburse for the National Board Dental Exam Parts I and II.
No, it isn't required. The Navy will allow you 18 months to obtain dental license in any state. You can actually practice dentistry in the Navy during this time (under a plan of 100% supervision), but keep in mind that, until you have a dental license, you will not receive Incentive Pay (IP) as a dentist. HPSP is only concerned with getting you a DDS. Obtaining a license is separate from obtaining your DDS, so they will not reimburse for WREB or any other regional licensure exam. NBDE Part I and II is required to get your degree, which is why HPSP will reimburse for those.