Okay, wait a sec. Those flappers allow air that is bled into the HE's (head exchangers) to exit i.e. there's always a flow of air through the HE's. This helps keep that part of the system from getting too hot.
Air-cooled VW's use the exact same system.When you 'turn on' the heater, air is sucked from the engine bay then pushed through the HE's. You cannot get CO or CO2 or NO or other engine exhaust into the HE's unless it's from the car in front of you. If the HE's are like mine and not fully sealed to the exhaust pipes then you'll simply lose air flow out these leaks and receive less air into the cabin since the HE's will be PRESSURIZED with the air coming from the engine bay

Any smells you're getting would be coming from stuff burning off within the engine bay. Again, if your HE's are like mine and you have oil leaking from your engine then you can get oil inside your HE's and this will cause a bad smell (as my g/f told me once, "You smell like car."). Also, oil leaking on the exhaust and HE's will burn off and cause smoke/fumes. If such fumes are generated at the front of the HE's, like the area where the lower engine tin ends, or oil leaks on the engine itself that are under the engine tin, then those fumes can get sucked in to a leaky HE where the air enters the HE from the fan housing. It doesn't take much at all to create a bad smell.
On replacing/re-installing those parts, YES, put them back in even if you don't use your HE's! And that's not only my opinion but that also of a certifed VW dealership mechanic of 25+ years (those years of air-cooled VW's, BTW). If you don't want to use your heater, fine, remove the flexible hose that connects to the firewall. Of course, if you run a header (no HE's) then this arguement is moot.
BTW, my engine and new tranny are no longer dripping oil so I now have a non-smelly -- but still leaky -- heater