Yes, I also believe it is a booster exhaust. You can see the “Barco” flexible pipe joints coming up from behind the trailing truck and running under the boiler. Not all NYC Pacifics had boosters and not all were piped this way behind the stack. Some were piped into the engine exhaust jet in the smokebox and I believe others were piped into the feedwater heater to recoup some of the heat. Perhaps if a booster was added to the locomotive at a shop rebuild it was much easier to pipe the exhaust along the outside of the smokebox up to the stack.
J3a Hudsons had a separate stack in front of the usual smoke stack to exhaust the booster. There were many variations of the K class Pacific over its years of construction from 1911 to 1925 plus many modifications during rebuilds.