From FCOM 1.36.20 (pneumatic, controls & indications, overhead panel)
ENG 1 and ENG
2 BLEED pb sw
ON:
Bleed valve opens if :
Upstream pressure is above 8 psi.
APU BLEED pushbutton switch is off or APU bleed valve is closed.
There is no onside wing or pylon leak, and no overpressure or overtemperature has been detected
The ENG FIRE pushbutton has not been popped out.
In your scenario the APU bleed Pb is not off therefore the engine bleed valve will not open.
Hope this helps!
TTO