Yes, the protection diode turns the AC into pulsed DC and the capacitor before the regulator smoothes out the voltage somewhat. As long as it stays above about 7V the regulator should be able to give you fairly clean 5V DC. Even if it dips, the Arduino can run at lower voltage. It's guaranteed to work down to (I think) 3.8V at 16 MHz but will probably work even below that (like 3V).