In a standard wlf- game setup, if you're the militia, is it sound strategy to fire off a random shot on N1?

Objectively, no, especially in wlf- games.

At the start of the game the village is (almost) always in the majority and, as a militia, its extremely unlikely that you will have any way of identifying who a wolf is based on a few hours of D1 conversation. As such, it's more likely that you'll be shooting a villager than a member of the wolfpack.

Probability aside, even if you get lucky and hit a wolf, it can offset the village for the next day; it is unlikely that you'll be able to validate the kill for at least one more day and there will always be players who disagree with your choice to kill. This gives the werewolves an opportunity to push for a (probably justifiable) mislynch against you, meaning that the village could end D2 with 3 villagers down instead of 1.