Delaying to do fellowship is not common, unless there is an immediate shortage of that speciality.
You'll have to contact the Army speciality leader (MD who is in charge of surgery) and inquire if he/she anticipates a shortage or need in your fellowship interest.
A couple of notes of military pay for physicians to help you make your decision:
1) About 15-20% of your pay will be exempt from federal, state, and FICA/SS tax because this is an adjusted allowance for living and house.
2) About half of your pay is "special pays" which is not subjected to FICA/SS tax (which is a big discount). Special pays are basically cash bonuses given each year.
3) If you can claim a state of residence where military people are not subjected to state tax, then your complete income is not subjected to state tax.
With the above consideration, your starting income as a surgeon will likely be around $110, but your take home amount is equivalent to someone who makes $150 and pays all of the above taxes.
I'm not sure about the FAP not existing. I'll have to wait and see. Congress has the power to change their minds.
Good luck!