Well it depends on what the requirements are of your program and whether they will accept you. It has been done that Non-ACGME accredited fellowships have done in 4th year, as there is technically no official requirement to have finished residency or be BE in order to do it. Now Austen Riggs does require you to be BE, but I wonder if you showed a a particular commitment to psychoanalytic therapy and had for example won some related awards, published some papers/cases, read widely, started your own analysis, and already seen a number of patients for analytically informed work or done something innovative like leading a Balint Group for medical students etc whether
It could of course be that they require you to be BE or billing or other functions but why don't you ask and find out?
The other thing is, though training might feel like it's forever and you have (presumably) those loans to pay off - 3 1/2 years is actually an incredibly short time to learn psychiatry well - there are all sorts of things you can learn in 4th year that would be enriching if you wish - for example developing your teaching, leadership or administrative skills, working in a subspecialty you don't really have an interest in, international electives etc. The best way to learn something is often to do something else! That might not make sense but you can learn an awful lot of psychiatry from literature, there is a lot more psychoanalytic (particular group and organizational processes) in an MBA than you might think, you learn much about the nature of good and evil in prisons, and I feel I see all of mental life in the emergency room...
Anyway, you may find that you hate having your every movement and utterance analyzed, dissected, and chopped up further until there is no meaning left.
