I definitely think it's possible, but it's a little bit complicated.

I was looking through different types of DID alters, and I think the one that would fit Mademoiselle best is called an "introject", which is an alter based off an outside person/figure. Introjects often times can be based off a family member and provide a positive influence on the system. (They also can be negative to the system but that doesn't seem like Madonee). We know that Mademoiselle is a lot more prominent in ! era stories, and in !! era she shows up a few times when Shu needs her help, but she's starting to be a lot more absent. Tsumugi makes a mention of this in Magic Halloween, but from the perspective of an outsider who doesn't understand what DID is. Tsumugi instead seems to think that Mademoiselle is some sort of "safety blanket" that Shu needs to outgrow. In a sense, I think he's not entirely wrong, as Mademoiselle is less prominent in !! and has a tendency to show up moreso when Shu needs her for something (like when he had to give a white day gift to Eichi, she was so absent during winter of !! that it makes this stand out more to me).

So how was Mademoiselle formed? When did it happen?

In Victoria, Natsume says that Shu entrusted a part of himself to Mademoiselle because of his execution on stage. I don't think this is when Mademoiselle was "created", rather when Shu needed to start relying on her heavily because of the trauma. We know Shu was bullied a lot as a child, so the initial trauma that sprung Mademoiselle into life may have actually happened before the execution. I think a form of Mademoiselle might have existed even before Kuro's mom passed away. In Nocturne, near the end where Shu asks Kuro to hold Mademoiselle, Kuro snaps at Shu and tells him to stop talking "feminine" and like his mom. Shu replies that it's "merely playing house" like they used to do when they were children. This makes me suspect that some form of "Mademoiselle" was around for the two of them to interact with as children, but likely under the guise of play time. However, when reminiscing on how he first met Mademoiselle in Victoria, Shu does mention that he used to talk to her (the doll), but she couldn't respond back to him. But he could tell her anything, and she would listen. I think he was having a one-way conversation with the Mademoiselle alter, and didn't really have a name/word for it yet to describe what was going on. He said talking to her made her begin to "come to life" by reacting and responding in turn. Mademoiselle reacts to the story by saying that she wants to help Shu fully experience and enjoy the world, and to return the love that was bestowed upon her.

Mika does think in Victoria that he "got to meet Shu before Mademoiselle did", but I'm not entirely certain that's valid. We know in Machina that Shu doesn't need Mademoiselle to be present in order for them to talk to each other, so just because he wasn't physically holding her doll (that's the reason Mika thinks he met Shu first), doesn't mean she wasn't around. Shu says he met Mademoiselle "before puberty", but that's a bit vague for the age...

Mika tells Mademoiselle he doesn't know a lot about her in Victoria. She in turn replies that neither her or Shu really know too much about her. When she talks about herself, she seems to be referring to the physical doll, however... what she says is a little more interesting. "I am Mademoiselle, a doll whose name holds no more meaning than simply a "little girl" .... before I was able to be given a name, I had already been case aside, you see. It's possible, that I spent such a long, long time all by my lonesome, that everyone eventually forgot my name... All that time, by myself... until Shu-kun found me." This would fit with the idea that "Mademoiselle" existed when Shu was a small child and then went away for a bit when she wasn't needed anymore (like when Shu went to middle school) and came back again during the execution. But the little girl part makes me think that while she does talk like Kuro's mom, she isn't a 1-for-1 copy, moreso based on Shu's perception of Kuro's mom / femininity back then.

Shu mentions that he burned all his pictures in his childhood from when he dressed girly, I wonder if that was him making a concious effort to supress Mademoiselle somehow? Because that would have likely been after Kuro's mom passed away, perhaps it was painful having Mademoiselle around? He wanted to grow up, and not rely on her.... until he needed her again.

Of course, there's always the possibility that Mademoiselle as an alter formed when Shu was executed on stage. There's a whole bunch of articles I read about how DID forms / when it happens and I'm going to say outright I don't know much more than the average person who googles things knows about DID. Some sources say that while alters can form later in life, the initial condition needs to happen early in childhood, while other sources say that a significant traumatic depersonalization event can cause someone in their teens to develop the disorder. Going off the first one, that would imply that Shu's condition developed in childhood (likely from the bullying) and either Mademoiselle formed then, or he had some other alter / possible fragments that formed initially, and Mademoiselle formed later at his execution. OR, for the second one, since the way ex-Valkyrie's execution went was focused on them being humiliated on stage for not being perfect (Shu made them pre-record their voices to stay in control and make sure everything was perfect. Humans are flawed, dolls are perfect), that could have de-personalized him towards humanity / wishing he/they could have been more perfect, like dolls, and developed his doll alter Mademoiselle.

I'm not a psychologist I have no idea but these are just speculations. Please don't take anything I said in bad faith.

I feel like Mademoiselle has many roles, not just "kuro's mom" / helper for Shu. She was a little girl / his friend when they first met, then she provided the comfort of Kuro's mom, but he has also described her as a sort of "soulmate" though I don't think there's romantic connotation there, morseso that she is just someone who fundamentally "gets" him. Though there is the connotation in Hermitage where Mademoiselle is "jealous" of Mika to an extent. Jealous of what, Madonee...? ._. Anyhow, he is very protective of Mademoiselle, not wanting her to be exposed to human lechery such as wearing revealing swimsuits / seeing Mao right out of the shower. I think in a sense Mademoiselle can function of the idea of "woman" to Shu, which was formed a long time ago when he was a child and upheld into adulthood.

What's nice about Mademoiselle, is she takes some difficult conversations for Shu. She's kind and caring and a lot nicer to Mika than Shu is. I think this is because Shu has issues verbalizing praise/his feelings for Mika, specifically because of how things ended with Nazuna. Shu used to constantly wax poetic/praise Nazuna, and that caused Nazuna to not really accept it as well, thinking it was undeserved, and it pushed him into feeling like he couldn't meet Shu's expectations, eventually driving him to be selectively mute because he felt Shu would disapprove of his new voice. So Shu doesn't want to make that same mistake with Mika... But Mademoiselle can be nice and kind and sweet to him, because Mademoiselle isn't entirely Shu, and that's part of her role. She's comforting, and because Shu cares about Mika, that extends to Mika too. It's noticeable from how Mademoiselle talks to everyone, adding -kun and -chan to the ends of their name as a sense of familiarity / making her seem like more of an older figure to them. She can help Shu express that softer "feminine" side of himself that he has a complex with.