Metallic smell when HVAC Unit. fires up. What could it be?
I think you need to find your way into the heat exchanger and look for "foreign" matter to clean out.

Let me walk you through what is going on here.
The initial fan noise you hear, is the draft inducer blower, and it does exactly what you suspect.  It should take air from either your intake air vent, or older furnaces would use the ambient air of the room.  After the ignition logic does it's safety thing, then the main burner kicks in with that big whoosh.  The main blower will come on soon as well.  At this point the flames are burning in a combustion chamber where the exhaust should go up your chimney or exhaust vent.  You should not smell this for more than a minute if everything is drafting properly.

The heat exchanger is the above the flames, and the main blower moves return air over the other side of these channels and that is the heated air sent out the rooms.

Now when this metal heats up there may be some odors depending on how clean they are and what condition they are in.  That would be in the air flow, so that your don't smell that everywhere is telling.  A bad possibility would be a hole in the heat exchanger where combustion products could leak over.  A CO detector is highly recommended.