Yes. Probability of reaching a game position is a product of the per-move probabilities, so adding them up tells you how much "luck budget" you need to reach th

Yes. Probability of reaching a game position is a product of the per-move probabilities, so adding them up tells you how much "luck budget" you need to reach that position, or equivalently, how much information is required to pick that position out of the distribution over positions reached (by a particular player, in this case).