What would happen if I were to connect an Arduino to a 9V 500mA AC adaptor instead of DC? Would it just not work? Would it explode in a huge ball of flames? What would happen?
If you connect it to Vin then there is a series diode fore reverse voltage protection that would act as a half wave rectifier on most arduino boards. This would turn it into DC but with quite a bit of ripple. I would be tempted to add an extra large electrolytic capacitor on the cathode end of that diode. On the Diecimila there is a 100uF in this place. I would be tempted to add another 1000uF or so. Remember 9V RMS is about 13V peak so there is a dissipation issue if you draw much current.
In my case, when I did that, it let the magic blue smoke out of a caps for the on-board voltage regulator. I didn’t pay close enough attention to the wall wart, it said 12v AC, not DC.
it said 12v AC, not DC.
12v AC gives you 17 volts peak. So you are feeding it with 17v.
I suspect that your supply gave you even more than 12v due to the light load and exceeded the voltage rating of the input capacitor.