Is the potential point scoring of an extra turn a significant factor, or is it swamped by the variance in the actual VP values of the monsters throughout the rest of the game?
For the most part it's swamped by variance in the monster deck. The first player bias of any game is inversely proportional to the number of turns taken in a game and is larger in engine building games. In Dominion it's huge because each player takes maybe 14 turns, and it's an engine building game, so that last turn is enormous. In Ticket to Ride, the first player advantage is barely noticeable. Some people get 40 turns and others get 41, and you can't do anything new on the 41st turn that you couldn't do on turn 10.
Thunderstone is somewhere in between. Each player gets more like 20 turns and there's less engine building than in Dominion. Note that in a game with more players, each player takes fewer turns (due to the constant size of the monster deck), meaning the first player advantage is more pronounced.