No, it won't. And there is an interesting thing in the manual that talks about this. It doesn't immediately start charging when the power comes back in, to prevent this situation where there may be many Teslas in a neighborhood in some places and they all start a really heavy draw as soon as power is back. So when the car detects that charging power is connected again, it waits for a random amount of time up to a few minutes I think before restarting charging to make sure it doesn't slam the grid as soon as it comes back on.