How often do airliners fly without their APU fitted?
Very rarely. I suspect what BUSH BABY was refering to, was operation with APU inoperative, but not removed.
If the APU is removed the APU compartment have to prepped (various ducts, electrical connectors and fuel lines blanked off). The CG will of course also change - an APU can weigh approx. 350kg - and will have to be compensated for.