First strikes definitely factor in the calculation. However keep in mind the Drill 1 promotion is very weak because it merely gives one first strike chance. Drill 2 and 3 are a bit better.
Let's say longbowman has 4-7 first strikes (this would be true if it were Drill 4). 3 of the first strikes are only possible first strikes. To find how many of these possible first strikes are converted, the game picks a random number between 0 and 3 (from a uniform distribution to be exact). The longbow would then enjoy a number of rounds (4+rand(0,3)) where he is immune to taking damage.
Turns out first strikes are a bit complicated in how they go into the odds calculator but I can assure you the person who wrote the one in-game, Deep0, did it correctly. The most it could ever be off by is less than about 0.1%.