The EVSE should contain a GFCI, if not your circuit should include one. I have the Square D EVSE and it includes a GFCI.
As far as power outages, the relay in the EVSE will shut down immediately and disconnect the circuit from the car. The relay is the loud thunk you hear when the charging starts. There is no need to actually flip the breakers as the car and the house circuit are separate until charging commences. The relay ensures this separation.
When the power comes back on, the EVSE will power up and request a confirmation from the onboard charger before releasing the relay and commencing with charging.
This is basically the whole purpose of the EVSE and why connecting a the car directly to an outlet is not recommended. I'm sure there is a way to trick the pilot signal so the car accepts the charge from a direct plug in connection, but this would defeat all of these safety measures. That is why I think the EVSE should actually be called the Safety Switch but then that would probably cause all kind of lawsuits. So, EVSE it is.
I had my car plugged in last night during a viscious thunderstorm and had no problems. The J1772 connector was wet so I checked my EVSE and pressed the stop button even though the relay had already disconnected the circuit after the charge was complete. I would definitely advise stopping the EVSE before removing the plug. Then you know you are definitely dsconnected.