I started up the worldbuilder to do some tests on this. A drill 4 rifleman versus an unpromoted rifleman shows a 78.7% chance to win, so the calculator does include first strikes.
A drill 4 redcoat versus a combat 2 rifleman shows 87.7%, and a combat 4 redcoat versus a the same rifleman shows 89.6% chance to win. That seems like a typical situation to me, and it looks like drill really isn't anything special in the open field where the redcoat has the advantage.
How about when attacking a city? A rifleman with city garrison 2 and a 25% bonus for being fortified will defend a city with no cultural defense. The drill 4 redcoat has a 28.9% chance to win. A redcoat with drill 1 and combat 3 has 34.1% chance to win. The combat redcoat, which you can build, has better odds than the drill redcoat, which you would have to upgrade. A redcoat with city raider 3 has an 88.0% chance to win this fight. Now that's an upgrade worth doing. A redcoat with drill 1 and pinch has 29.9% chance to win. You can draft a unit with those promotions, and it has better odds of winning than the drill 4 redcoat.
So I really don't see any reason to do a mass upgrade of drill 4 crossbows. First strikes are good for minimizing damage against weak enemies; a drill 4 redcoat would be great for defending a city against lots of musketmen, but I don't think it's practical in a real situation.