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.