[susan53]

Same as above. With uncountable/plural nouns, where implicitly I want to know "how many", then I'd use the quantifier. Think how the conversation would naturally develop - the reply would almost certainly specify the number :
- Have you got any children?
- Yes, a son and two daughters 7 No, none

It's only where the number is irrelevant that I think I would drop the quantifier :

Have you got children? Omega 3 Fatty Acids are an essential part of their diet.
Have you got children at University? Please help me with my survey ..

That's how I think I would use it (and I suspect many other people). However, Google it and you will often find the quantifier dropped in implicit "how many" contexts too:

Objectives of the research : To gain insight into the feelings and experiences of midwives who do not have children of the effects of a negative response to the question, 'Have you got children?', on the midwife's perception of herself in the midwife/mother relationship and to formulate strategies which promote successful midwife/mother relationships.

Two points about this : a) it's formal written English rather than the conversational style that I've used in my example; b) it's from an Australian site. In other words, variety of English may come into play here, and the choice of quantifier/no quantifier may be affected not just by meaning (as I've argued) but also by stylistic or regional variety.
You'd need to do some research with a corpus to decide definitively which of the three factors are most relevant.