FAA Pilot EXAMS
No you will not be required to take the FAA Pilot exams for your military flight training. You will take exams, but they are Military exams that cover the same material as the FAA exams plus the military specific information from NATOPS, OPNAV 3710 and other Military only Pubs. So unless you are on the verge of earning a Civilian Pilot's license and want to continue civilian training there is not much point to spending the money to take the exam. I've taken most of the Civilian exams and did not find them helpful in Primary or advanced so far.