I do not expect it to fire all the time, or for a player. However, in 30 continuous attempts Charles got an heir within the first 10 or 15 years, sometimes even the first 5 years. I think this is worth noting because Burgundy does not seem exempt from "heir events" that might fire for the player, meaning it's very unlikely they won't get an heir. I think the previous system in which Charles was made a general made the BI more likely to fire.
31st time. Didn't fire again.