On the 727 if the APU is out, you're dead in the water, so to speak. You cannot start the engines or refuel the aircraft unless ground power, GPU, is available and you have an ground air source to start at least one engine.
In fact, unless modified, if you leave an engine running after landing, you still cannot refuel with out a GPU on the 727.
Oh, the APU on the 727 cannot be used in flight, ground operations only.