I'll try to answer your questions while avoiding as much PII as I can. I was recruited primarily for backstroke and secondary as a sprinter. I'll avoid specific times and the years of my recruitment because its not relavent to 2017. I can safely say that I would not be recruited today based on how fast the overall team as gotten. Again, look at the Navy Sports Website and compare your times. They recruit guys who can score points now in the conference championships. You should be faster than the junior national times minimum and inching closer to senior national times in hopefully multiple events. However, back in the early 2000's we were starting the up swing. I was speaking from personal experience in my first post about being recruited for sprinting. I was a case where I didn't get faster at Navy. I enjoyed my 4 years on the team but by the end I wasn't a factor for points.
I believe my initial contact with the team was via a questionnaire on the navy sports website followed by a face to face during summer seminar the year prior. Then throughout my senior year of high school I received calls and did the official visit. Living in a state that surrounded Maryland (as specific as I'll get), coaches would routinely go to large meets in the area. If you don't live that close, times are black and white so once you're on their radar they can keep tabs on you. If they are interested in you...then your application gets special attention paid to it and extra points are added on the admission board so absolutely your chances of getting in go up exponentially if you are a recruited athlete. The key is to make it easy on the coaches by having really good grades/test scores so they don't have to burn as much recruiting capital on you.
Hopefully this helps, again the information is out there on the navy sports website.