I doubt 20 kids would be enough to qualify. Most people of my grand parent's generation had around 20 kids. It used to be the norm.
However, in this exemple (Charlemagne), I doubt it unless he had a lot of bastard children.
In the example of my grandmother, she had up to 20 children (excluding those that didn't even make it to birth), but only 17 of them lived. The poor still had a lot of children, albeit with more issues, so I doubt the social capital would help here.
I have no idea, really. But this in an interesting conversation.
Do the math...this is clearly false.