Yes, several players from the Navy have made their way to the NFL. The most notable among them is Roger Staubach, who was picked by the Dallas Cowboys and played as a quarterback from 1969 to 1979. Staubach had an illustrious college career at Navy, even winning the Heisman Trophy in 1963. Other notable Navy players who made it to the NFL include Ed Sprinkle, Bob Hoernschemeyer, and Mike Wahle.
In recent years, the tradition of Navy players joining the NFL has continued. Malcolm Perry, a fan favorite, was selected in the 7th round by the Miami Dolphins in the spring of 2020.
Moreover, it's not just Navy; players from other service academies like Army and Air Force have also made it to the NFL. For instance, Chad Hennings from the Air Force was drafted by the Dallas Cowboys and Bryce Fisher also had a successful NFL career.
Interestingly, over 1,000 NFL players have served in the Armed Forces, with 995 NFL athletes joining the military ranks during World War II. This shows a significant overlap between the worlds of professional football and military service.