The answer is no.
Anyone can argue that an ex-President should have it, but the question of whether he does is pretty cut and dried. As of now, he does not.
The idea behind Executive Privilege is to allow the current President to do his job without fear of having someone peek at his notes, not to prevent others from knowing what he has done after the fact. That's why the choice of whether or not to invoke it lies with the current, not former, President. The caveat is that that is the way it is because of the Supreme Court decision back in Nixon's time, so it is theoretically possible that this Supreme Court could reverse that.