But you may run the APU for a while lowering fuel in one tank.
I suppose if you don't have any fuel in the CWT, APU fuel usage will not be offset by CWT fuel scavenging (where an electric CWT scavenge pump is fitted).
On 744s with hydromechanical scavenge pumps, is APU fuel usage a problem? Both 2/3 tank aft boost pumps are turned on during ground operations to feed the APU, but I heard somewhere that APU has a preference for tank 2 (fuel from tank 3 has to travel much further to get to the APU)