It looks like non scholars continue to have a slim chance of being promoted to BG.
One of my friends, from the old days, rose as high as Colonel, although he was a fighter pilot, good results, and graduated from NUS with a first class honours, while still serving the RSAF. Eventually, he was a Colonel, and at one point, Head of Air Intelligence.
Thereafter, he was a military attache, before retiring at age 50.