There is a general problem of deceitfulness in OD - people lie about how tall they are, how old, how recent their photos are, lots of stuff.
So for me, I don't really have much of a preference between women with DC or none. Women without will have more free time, women with will understand how precious my time with mine is and not to get jealous of it. Swings and roundabouts.
But if I went on a date with a woman who'd said she didn't have them, actually stated on her profile that she didn't, and never mentioned them in conversation until the date, I would be put off her for that reason. Not that she had kids, but that she misled me about them.
I can understand why she might do that, of course, but I think it's best to be upfront about it. It may reduce the size of your dating pool, but what's left are going to be better suited.
I checked the box which says I smoke, although I know it'll put many women off. When I quit, which I plan to do at some point, I'll uncheck the box and suddenly be a better person :) But there's no point not checking that box, and meeting someone who will be disgusted when I nip outside for a smoke on our 4th date or something, and never want to see me again.