Nope. Trained-CM is so fast you don't have time for engine-like considerations. For example, 6 Provinces by Turn 14. (Trained CMs beat trained Scheme.)
Okay, so it turns out that this is a really good best case and has a lot of support.
From what I can tell, the baseline strategy is buy a bunch of Candlestick Makers, buy training on them as quickly as possible, and buy green as soon as the Candlestick Maker pile is empty. This is pretty easy to simulate, and with that strategy, one averages 14.5 turns to 4 provinces, which is pretty good for such a mindless one - about the same as Double Jack.
This particular board happens to contain Scavenger and Governor, the former of which has a very high upside when placed in BM and the latter of which significantly speeds up any board: with Governor, 6 provinces in 14 turns is pretty bad and with Scavenger, a single case of it happening is unsurprising.
Also, you can 3-pile very quickly with trained CMs. In this one, my trained CMs beat trained Bakers. Once Native Villages were depleted on turn 12, I ran the estates and saved coin tokens for a last-turn Province. Since his deck only had one +Buy, I controlled when the estates would finish, and could time it to end when I had more VPs.
This is true whenever you have significantly more gains than the opponent, and in this case you were fortunate that your opponent did not play a more focused strategy. For example, a money strategy in which 3 Gears and 1 Dungeon are bought is able to buy 4 Provinces in on average 13 turns. Once again, although you won, the win significantly underperformed the board's potential.
Training + Candlestick Maker, although interesting and potentially proper on certain weaker boards, is just not that fast.