I suspect that in almost all cases it has already converged on a move well before sixty seconds, and so if forced by time pressure to choose a move before it has achieved the confidence it's looking for, it will probably still do the right thing most of the time (especially in the endgame, when the branching factor is cut down enormously). It just uses additional time because it has it. I would love to see a graph of AlphaGo's thinking showing certainty of time, and how long it was taking to come up with the move it ultimately ended up playing, and how that certainty evolved over its thinking period.
