Starfleet Acadamy does have scientific and medical divisions but I think people with degree level qualifications can simply take officer training. Isn't that also the case in the present day navy? I thought navy engineers were usually trained at outside institutions?
Indeed our own navy is like that here, down under. Many years ago I applied to the navy where I qualified for officer training. After waiting for, what I thought, was an ice age I joined the army instead as an infantryman. Idiot!
I now find that I am still qualified to join the navy as an officer as an administrator/instructor. Though nowadays I've reached a point in my life where I'm no longer interested in serving in the forces...