To be a little different I decided that cadets all train together with specialty classes depending on if they will serve on ships, in the air force, on the ground piloting mechanized infantry, or if they are magic users.
Aside from no magic users, welcome to the Canadian Forces.
These days, all enlisted Regular force (ie, not the Reserves/militia) personnel attend the Canadian Forces Leadership and Recruit School in Saint-Jean-sur-Richelieu, Quebec. After they complete Basic Military Qualification, which is common to everyone regardless of what branch they end up in, they go off to their separate training facilities and bases across the country.
For officers, officer-cadets attend one of the Canadian Military Colleges. There were three when I was in in the late 80s/early 90s: College Militaire Royale de Saint-Jean, also in Saint-Jean-sur-Richelieu, Québec, which I attended; Royal Roads Military College (RRMC) just outside Victoria, British Columbia; and the original, the Royal Military College (RMC) in Kingston, Ontario.
(Aside: in 1995 RRMC was closed as a military college and is now a civilian one; CMR was also closed in 1995 and became a civilian college, but in 2007 was re-opened as a military college using part of the now-civvie campus.)
Okay, so the way the colleges worked is that all officer-cadets, regardless of where they planned to go (Maritime Command, once again the Royal Canadian Navy; Mobile Command, now again the Canadian Army; or Air Command, it also now bearing its former name of the Royal Canadian Air Force) attended the same classes--depending on what degree they were working toward--were in the same squadrons, and we wore the same college uniform. We also had branch-specific uniforms that we wore when we did our specialized training over the summers: tan/green for us superior army types, black/white for the naval wogs, and blue for those who wanted to fly planes. The only time we wore them at the college were the specific days dedicated to a particular branch, so on naval day, for instance, all the naval types wore their blacks or whites while the rest of us stayed in the normal college uniform.
Additionally, the first summer in, all officer-cadets (and all future officers who would skip the colleges because they were, say, doctors and thus would directly get commissions) attended CFOCS ("see-fox", the Canadian Forces Officer Candidate School) at Canadian Forces Base Chilliwack. Again, regardless of future service. If you failed CFOCS, you were out. After that, summers were off to whatever base providing the specialized training for your branch; military engineers, for instance, did the course at Chilliwack, infantry went to CFB Gagetown, and so on.
Other than the summer training periods where you'd go off to do branch training, all cadets received the same military education and training at the colleges and CFOCS. This also meant that people could shift branches; we used to joke that the majority of Canadian warship drivers were wannabe-pilots who couldn't make flight school due to poor reflexes or bad eyesight. If someone wanted to be a military engineer but didn't have the academic wherewithal to get the required engineering degree, it was theoretically possible for them to switch to, say, infantry or armour, or some other job where a BA would be enough. It was rare; usually if you flunked the academics you were out, but I did see it happen.
So there's nothing particularly odd about your suggestion; it's been successfully done in real life.