It may work. It will only provide power to the Arduino on the positive half-cycles of the AC waveform. During the negative half-cycles, the diode in series with the 2.1mm power jack will prevent current flow.
This means the capacitor at the input of the linear regulator (47uF is specified on the schematic) must supply power to the Arduino for the majority of the time while it is in operation. Assume the Arduino consumes 20mA (optimistic) and does not power anything else. The capacitor voltage changes by dV/dt = i/C = 0.02/47e-6 = 0.425V/ms. The negative half-cycle of a 60 Hz waveform lasts 8.33ms, so the capacitor voltage will drop by 3.55V in this time. It will also drop more during the positive half cycle until the voltage is high enough to both recharge the capacitor and power the Arduino. But since your AC voltage is so high, it might just work.
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The MegaRAM shield: add 128 kilobytes of external RAM to your Arduino Mega/Mega2560