Highly unlikely, but there is never any absolute in the military. Transitions between individual aviation communities are rare, unless there is a service-wide transition to a new aircraft, and they are pulling from all communities. No doubt there are anecdotal special cases. Test pilots might fly a range of air frames, but that's a different career path. Air Wing commanders get to have some fun too, usually getting qual'ed in all the aircraft types they will command. That's a billet w-a-a-y down the career path, post-squadron command.
"Halfway through your career," and you're in one type of airplane, then your mid-term career focus is command of a squadron of those planes. You (and the Navy) will expect to have a depth of experience and practical knowledge, as well as advanced skills, in that airframe. The Navy will have invested years of training in you by that time. Why would they switch you to another airframe, where you would be a more senior officer with less experience in the airframe than officers junior to you with a few tours in that same squadron? It would also cost the Navy money to retrain you in the new bird, and that's always a good reason to not do something.
Always good to ask these musing kinds of questions... there is lots and lots of time, and I would bet by the time you've amassed all kinds of squadron patches on your flightsuit, you wouldn't trade it, especially when you're having fun at an instructor pilot tour or taking newly-reported pilots under your wing.
My comments are based on observations from spouse's 26 years in naval aviation, brother-in-law's 24 years in naval aviation, my own pass through an aviation squadron in a non-flying billet, and several years of watching new generations of pilots move through their careers from initial pipeline to squadron tours.
The only transitions I've personally seen are early on - a USNA sponsor son who went Navy air, got helos, but applied for jets when the Marines opened up slots just before he started helo basic, cross-commissioned, and is happily flying Harriers now. Another USNA sponsor son was in the jet pipeline, had a hernia issue, was NPQ from jets (pulling G's problem) and they switched him to P-3, where he's happy to have found a home.
