I highly doubt a society could continue with only a third of the population having children. The part about a third becoming religious might be possible (although even that seems unrealistically high), but I have a hard time believing a third of people remained lay people in the single state.
We would need some evidence of all of this too, of course.
It was perfectly possible in the times where families had 6-10 children per family. The idea seems to be from using the Trinity as a metaphorical lens.
I'd like to add, Benedictines had the rule "8 hours of labour, 8 hours of praying, and 8 hours of sleep", cutting every day into 3 perfect parts, duty to self, duty to God, and duty to the community.
In the medieval era, there were also 3 classes : those who prayed, taught, etc (Ecclesestials), the rulers who fought and defended the country, and the labourers.
The number 3 can be used in infinite variations such as those.