My experience with 2 AOS's under my belt is the smoking comes later. In both cases it was a last stage -- well as last I was willing to let things go -- symptom.
In the first failure there was hesitation, rising and falling idle speed, I can't recall now if there was a CEL and if so what the DTCs were, a lot of vacuum at the oil filler tube.
In the second failure there was just a CEL with one or more DTCs the numbers I forget now but they had my thinking MAF but I can't recall why now, either.
This went on for a few days as I was making my way east from CA to MO. I made it to MO alright but the next day when I started the engine the smoke came billowing out of the exhaust and didn't stop. It was then I realized the errors were related to the AOS not the MAF.
There is kind of a test to eliminate the MAF. Disconnect it at the wiring harness. Clear the DTCs to reset the fuel trims among other things. Then just drive the car normally. You have to drive it more than around the block. The engine should be up to temperature. I would advise you to avoid straying too far from home and remaining in good cell phone coverage.
Also, pay attention to the engine. Should it start to act up show any signs of untoward behavior shut it off ASAP and have the car flat bedded to a dealer for attention by a pro.
If the MAF is not the cause of the misfires and other errors some of these should come back.
You'll need of course a scan tool one that you can use to clear DTCs and read codes. The CEL may come on with the MAF disconnected but this can be from the MAF being disconnected, not the original symptoms you are trying to diagnose.
If the CEL and DTCs come back with the MAF disconnected it is probably not the MAF at fault.
If the CEL and DTCs do not come back then connect the MAF and clear the DTCs again then drive the car again. If the CEL and DTCs come back, the MAF is pretty much confirmed.
Handle the MAF and its wiring with care. Those pins in the connector lead directly to the MAF. A static discharge into one of them ruins the MAF. And the sockets in the connector lead directly to the ECU. Static discharge into that and oh oh...
Also, the pins can bend over or break. Working with electrical connections on a used car requires a combination of gentleness and strength.