I don't think so, actually! We know that from age two onward, she was growing up in the Golden Gate Girls' School, which was like combination orphanage and boarding school, and we also know that there were at least a handful of other girls Carmen's age around while she was there. (Coincidentally, I always think that picture is sort of telling in that you've got these five little girls standing in a line, and yet they're still pretty evidently split into two pairs of two, and Carmen in the middle with the bear. Even as a kid she was a loner in a crowd.) So I don't think she'd be eager for a sibling her own age, because her classmates were already acting in a similar capacity for her, and I don't think she'd envision a younger sibling because of how independent she was as a kid; I'd imagine she'd have seen them more as something slowing her down than an asset.

As for older siblings...I don't think she'd really want a sister, but that might be because most if not all her older influences in canon are male, and she seems to take better to Playing In The Boys' League™, as it were. An older brother, though...if it were going to be anything, I think it'd be that. In a sort of "the Mycroft Holmes to her Sherlock"-y sort of way.

But no, by and large she didn't think a lot about siblings. Parents, yes. And possibly she thought about siblings in a manner sort of incidental to that — "I wonder who my parents are, and if they have kids other than me, and where they are if I'm here" — but she probably didn't dwell on that too much because let's be honest, thinking about that too much would only lead into questions of "so why didn't my parents want me, then?" and that's just super depressing.