I think an important point was brought up by the Google engineer in the beginning of the game: Humans usually consider moves that put them ahead by a greater margin and base their strategies on that, while computers don't have that bias.
Building on that, I suspect that if AlphaGo thinks it has a 100% chance of winning with any of several moves, it has no way of distinguishing between them and chooses effectively at random. The longer that goes on - and once it hits 100% chance of winning, it will be that way for the rest of the game - the more chances it has to pick bad moves. As long as the move isn't bad enough to ruin its 100% chance of winning, it can't tell the difference between that and a good move.
(This also applies without a 100% chance of winning, as long as its chances of winning hover near the highest percent it's able to distinguish.)
I doubt the value network ever outputs a literal 100% chance of winning, it would at most be a lot of nines.
Even if it did output an actual 100% chance, AlphaGo would still end up picking moves favored by the policy network, so it would probably just revert to playing like it predicts a human pro would.
Once it gets to enough nines, its monte carlo trees will run out of sample resolution. If it can resolve to three nines, then a 99.93% win branch has a 70% chance of being reported as 99.9% and a 30% chance of being reported as 100%. When all the branches here get rolled up, they report some average around 99.93% but not necessarily exactly it. This propagates upwards in the tree, adding more meaningless digits. Adding the evaluation network in increases the number of decimals, but doesn't really change the effect.
It's similar to how ray tracing renderers start to return weird speckle patterns when the room is dark enough.
And the policy network chooses branches to investigate, not which one to choose. It adds sample resolution to places pros might play, but doesn't add to the estimated probability of winning.
Edit: Actually, since places pros might play have higher sample resolution, they're less random. So worse moves get worse evaluation, and a higher chance of leading the pack. This might actually bias AlphaGo to play some pretty bad moves - but, again, this is all assuming it's going to win anyway.
