I do not have DID, but I do have severe PTSD, which includes dissociation and similar symptoms.
First, DID is not a personality disorder, even if it was called Multiple Personality Disorder. Personality disorders are a category of mental illnesses. It's an issue of technical terminology, but I think a good number of sufferers would be offended by the mistake.
It seems really unlikely to me. The big indication is the beginning of her first police interview. She knows a lot of details about her life. She doesn't seem to have any problems telling her life story chronologically. It seems unlikely that a lawyer would put much emphasis on having Patsy memorize this information and practice it. If she had DID, I would expect it to be fairly apparent in that section that there was something wrong with her memory.
She was asked about what medications she was prescribed. There are no hints there. It's pretty ordinary.
Another thing is that DID is typically associated with childhood trauma and develops while you're still a child. With how much this has been covered in the media, I'd expect people to have sold more stories of unusual behavior when she was a child.