I’d wager that the percentage is significantly lower than the background average

I’d be curious to see the stats, because it would be interesting to know if certain professions or volunteer positions attract these people (i.e. because of their proximity to kids).

Background checks really only work if someone has a history. Everyone is a law-abiding citizen, until they are caught, arrested, and convicted of a crime. We only know of the ones who are caught, and it’s not easy to catch these people.