Yes it matters how they became single because I'd want to know what kind of mess I'm walking into if I were to consider dating them.
If she got pregnant, told the dad, he didn't want it, she tried to force him into parenthood, so he left, and she became single? She can fuck herself because I'm not going to fill the role as the father figure in her child's life, and that's what she'd be expecting.
If she got pregnant, told the dad, he was ok with it, things didn't work out, he left, she became single? I wouldn't judge her right away but would still try to get to know that situation a bit more since he could have left for various amounts of reasons.
If conditions were as perfect as they could be and she didn't expect me to raise or pay for her kid, then I'd maybe consider it. I love kids, so I wouldn't be bothered having the kid around, and my personality isn't that of wanting to spend quality alone time with people outside of sex, so it's not like the kid would 'get in the way'.
She'd really have to understand that I'm the one who decides whether or not I want to take an active role in her child's life, though, and that I'm not a source of income for raising a kid I had no part in making.