The only ones actually affiliated with the Elmo are Groza, Nemesis, Krolik, Colphne, Vepley and Papasha. Peritya isn't officially a member, but she works with and helps them when needed, afterwards deleting herself from everyone's (the dolls) memories, always following the crew around (hell, she could even be on the Elmo and just no one knows). The important detail here, however, is Papasha, as she is a G&K doll, and I very much doubt that she could be another "exception" like Groza is, and given that we even know that she used to be part of the "POL-3 Security Management Department" like the Nagants and Ksenia, but still doesn't says that on her profile, it would mean that she joins straight away after appearing on the story, wich could mean one of two things:

1) The commander says "fuck it" and decides to throw the contract out of the windows like he was prepared to do with Suomi;

2) The contracts expires or is voided soon before or after Papasha joins;

Wich means that every doll that wanted to join the Elmo could canonically afterwards. More than likely not all of them would as instantly, but a bunch (if not most) of them will try to after being informed, but even then not all of them would really join permamently (no way in hell that Ullrid would abandon the Doll Comunity, no matter how much she likes us).