I can't speak with authority on the Navy specifically. I would recommend contacting a MS4 at USUHS or Radiology preselect intern for a more recent take.
But in general terms.... the military match can vary drastically from year to year and you are looking at applying 3-4 years from now. Currently the Navy is (I think) still on the downswing and training spots are harder to get. Absolutely no one knows if when you graduate it will be worse, better, or the same.
I'm not a civilian PD, but from what I have heard in discussions with my peers, if you are a decent applicant you will get a spot in the civilian match. It may not be a tier I program, but if you want to do Rads and that is your primary objective, then your absolute odds of success may be higher outside the military.
The risk you take in the military is that the number and type of spots will change based on the needs of the service at any given time. Those swing wildly around.
If you get lucky and time it right, it can be smooth sailing and you train in what you want. If not, you are a GMO or do your second choice residency.
I don't mean that to be overly discouraging, but as others have said - you have to understand and be ok with the fact that you give up all control over what you will ultimately train in. The Navy/Air Force/Army will decide if they need you to doctor, where, how much, and as what kind of doctor.
To give you an example, I went this route. When I applied to med school, Radiology was roses and they had so many slots they let anyone who applied have a shot. When I graduated there were 2-3 PGY-1 slots only (all AD, no sponsored or deferred) and non-preselects were being forced into a mandatory flight doc tour. By the time I graduated residency they were back up to something like 20ish combined PGY-1/PGY-2 slots.
I got pretty lucky, but it easily could have broken the other way.