The kind of really short careers you mention have traditionally been more of an Army thing. It’s possible to do Sandhurst, serve a satisfying tour as a platoon commander and leave in a fairly short space of time having gained valuable leadership experience and made lots of useful social connections to take forward. Other corps, and a handful of RAF and RN branches offer a comparable combination of quick training and early large-group leadership. But forget about flying, and in most branches the satisfying tours are a few years away.
Connections are the valuable commodity for anyone pursuing a second career; the Army wins on numbers in the City and (as TN suggests above) attracts a greater proportion of the already-well-connected to its ranks. It takes a certain degree of self-confidence to do what you are proposing... I suppose if you have it, then why not? But probably in the Army, I would suggest.