No, they don't do that either. To mention one data point, there's a founder in the current batch who has three small children and is a solo founder. I don't think YC cares about that sort of thing, other than that the group partners (the people who work most closely with founders) would do what they could to support them if they were getting overwhelmed.
When YC rejects an application it's because they don't think that startup (or that product/founder combination, let's say) is likely to become a big business. That's the theory, at least. Of course it's not going to be perfect in practice, but YC's success depends on getting it right, so there's a strong incentive not to just naively repeat the known, large-scale biases people tend to talk about (you mention age and marital status, one can add race, gender, class, education, national origin, and others).
Also, YC is pretty diligent about studying its failures—companies that applied to YC, were rejected, and went on to become successful—and if there were any obvious patterns in there, you can bet they'd be all over it. I'm not claiming that's sufficient to disprove bias but it must count for something.
I think the best way for you to ensure funding is to have revenue traction. One thing that trumps ageism (and all --isms) is greed. If you show revenue growth and traction, these greedy VCs will swallow all their rhetoric and blog posts, get down on all fours and wag their tails like puppies to get a whiff of your term sheet.
Note that Valley VCs are well-documented ageists: "Vinod Khosla told a conference that “people over forty-five basically die in terms of new ideas.” Michael Moritz, of Sequoia Capital, one of the most pedigreed firms in the tech world, once touted himself as “an incredibly enthusiastic fan of very talented twentysomethings starting companies.” His logic was simple: “They have great passion. They don’t have distractions like families and children and other things that get in the way.”" [1]