Probably not, just a defense mechanism that Kaguya have that whenever she's in 'trouble', she'll go back to a personality that keep her safe. Eg, the past Kaguya that is distant from everyone else.
Hey, that's multiple personality disorder's definition!
"Dissociative identity disorder is characterized by the presence of two or more distinct or split identities or personality states that continually have power over the person's behavior. With dissociative identity disorder, there's also an inability to recall key personal information that is too far-reaching to be explained as mere forgetfulness. With dissociative identity disorder, there are also highly distinct memory variations, which fluctuate with the person's split personality."
While she might have a DID, I personally does not see it as it is. Kaguya's 'cold' personality was just how she was bc of probably childhood neglect and abuse but she changed to the lovable person she knew because she met the president and the people in the student's council. From what she said in the last panel, Kaguya doesn't shows any sign of memory variations/loss and her personality is too similar for it to be 'distinct'.
Though who knows what will happen, I might be completely wrong.
Wait, wait, she really has multiple personality disorder ?