In a word, no, it is not required. However, having flight time or even a complete private pilot’s license could improve your chances of being selected in an otherwise very competitive process.  For one thing, it could be viewed as a demonstration of both your desire and ability to succeed in flight training. Private pilot training does begin to develop your “air sense,” and this can be an advantage in the early days of pilot training.  However, it is very likely that by the end of training, everyone’s performance will look largely the same.

It is also worth mentioning that the FAA recognizes military pilot training. That means that after you complete your military pilot training, you can go to the local FAA office, take a test or two, and get several FAA qualifications (including commercial and instrument tickets)–free of charge.