Maybe down to the APU manufacturer you have fitted but our definitely don't start without batteries when the GPU is on.
You get a fault light and no accel as the fault recorded on the CFDS.
p.s. From the Airbus training notes
APU START CONDITIONS
An electric DC motor starts the APU.
On ground operation conditions,the APU is started by the aircraft batteries or aircraft batteries in combination with Transfomer Rectifier Units (TRUs).
A start in flight is possible up to an altitude of 11900 m (39000 ft.) with the use of TRUs. A start in flight is possible up to an altitude of 7630 m (25000
ft.) with the use of the aircraft batteries only.
For successful APU starting on ground or in flight, both batteries PB
must be switched to the AUTO position according to Airbus
procedures.