I watched the APU Maintenance Page on a 744 today. The inlet door opened in 8 seconds (after selecting "ON" from "OFF").
Unless the APUC is very slow to run through its required prestart tests, I don't see the point of using the OFF to ON, then pause, then START technique specifically to save fuel.
Cheers.
NSEU
P.S. Note that this 8 seconds may not be for full open, but rather, the time taken to reach the 15 degree open mark which triggers the logic to allow start. On the ground, the 744 APU inlet door opens to 45 degrees.