Guys,
I think everyone's missing a much simpler point here, while poring over venturis and smoke procedures. Vilas, in this case, I think you're wrong.
The FCOM (DSC 36-10-20) doesn't really help because the diagrams are not to scale and are only schematics.
The Bleed Valve is bolted just inches away from the engine casing. Downstream of the Bleed Valve, the ducts then go to the pre-cooler (between the engine and the pylon), and then onward to the packs, routed via the pylon and wing.
If you have engine damage, it's almost certain that the engine would have shaken itself to bits and the attached ancillaries (like the thin-walled bleed ducts) would be damaged too.
Remember, these ducts are all downstream of the bleed valve. So if the APU is trying to supply air, the air will now leak thru these broken ducts on the side of the damaged engine, pylon and wing.
Two obvious issues with that:
1. You have a leak!!! Why force air into a broken duct causing overheating, structural weakening (and if the duct is damaged in the engine, you'll be blowing away the agent that you just discharged).
2. The APU is wasting it's breath blowing into a broken duct, and your pack will almost certainly not have enough pressure to operate.
In short:
Engine Damage -> Duct Damage -> Don't put air in a broken bleed duct!