I believe kids are born of a contract, so if a contract was never written, I imagine no kids could be born. So no it shouldn't occur as a random event.
That being said, I wouldn't be surprised if orphans and adoption were an option, allowing you to pick an older child later in your life, that fits the criteria you want. Rather than having to raise a child to be the character you wish to play later in your COE career. Personally I think the idea of having and raising kids is an awesome thing, and something I'll certainly be looking into.